Junge, Marius
Overview
Works:  38 works in 86 publications in 3 languages and 810 library holdings 

Genres:  Academic theses Conference papers and proceedings 
Roles:  Author, Editor, 958 
Classifications:  QA403, 515.2433 
Publication Timeline
.
Most widely held works by
Marius Junge
Mixednorm inequalities and operator space Lp embedding theory by
Marius Junge(
Book
)
13 editions published between 2009 and 2010 in English and held by 241 WorldCat member libraries worldwide
13 editions published between 2009 and 2010 in English and held by 241 WorldCat member libraries worldwide
Theory of Hpspaces for continuous filtrations in Von Neumann algebras by
Marius Junge(
Book
)
10 editions published in 2014 in English and French and held by 173 WorldCat member libraries worldwide
We introduce Hardy spaces for martingales with respect to continuous filtration for von Neumann algebras. In particular we prove the analogues of the BurkholderGundy and BurkholderRosenthal inequalities in this setting. The usual arguments using stopping times in the commutative case are replaced by tools from noncommutative function theory and allow us to obtain the analogue of the FeffermannStein duality and prove a noncommutative Davis decomposition.Provided by publisher
10 editions published in 2014 in English and French and held by 173 WorldCat member libraries worldwide
We introduce Hardy spaces for martingales with respect to continuous filtration for von Neumann algebras. In particular we prove the analogues of the BurkholderGundy and BurkholderRosenthal inequalities in this setting. The usual arguments using stopping times in the commutative case are replaced by tools from noncommutative function theory and allow us to obtain the analogue of the FeffermannStein duality and prove a noncommutative Davis decomposition.Provided by publisher
H[infinity] functional calculus and square functions on noncommutative Lp̳spaces by
Marius Junge(
Book
)
9 editions published in 2006 in English and French and held by 171 WorldCat member libraries worldwide
We investigate sectorial operators and semigroups acting on noncommutative Lpspaces. We introduce new square functions in this context and study their connection with H[infinity] functional calculus, extending some famous work by Cowling, Doust, McIntoch and Yagi concerning commutative Lpspaces. This requires natural variants of Rademacher sectoriality and the use of the matricial structure of noncommutative Lpspaces. We mainly focus on noncommutative diffusion semigroups. We discuss several examples of such semigroups for which we establish bounded H[infinity] functional calculus and square function estimates. This includes semigroups generated by certain Hamiltonians or Schur multipliers, qOrnsteinUhlenbeck semigroups acting on the qdeformed von Neumann algebras of BozejkoSpeicher, and the noncommutative Poisson semigroup acting on the group von Neumann algebra of a free group
9 editions published in 2006 in English and French and held by 171 WorldCat member libraries worldwide
We investigate sectorial operators and semigroups acting on noncommutative Lpspaces. We introduce new square functions in this context and study their connection with H[infinity] functional calculus, extending some famous work by Cowling, Doust, McIntoch and Yagi concerning commutative Lpspaces. This requires natural variants of Rademacher sectoriality and the use of the matricial structure of noncommutative Lpspaces. We mainly focus on noncommutative diffusion semigroups. We discuss several examples of such semigroups for which we establish bounded H[infinity] functional calculus and square function estimates. This includes semigroups generated by certain Hamiltonians or Schur multipliers, qOrnsteinUhlenbeck semigroups acting on the qdeformed von Neumann algebras of BozejkoSpeicher, and the noncommutative Poisson semigroup acting on the group von Neumann algebra of a free group
Hypercontractivity in group Von Neumann algebras by
Marius Junge(
Book
)
10 editions published between 2017 and 2018 in English and held by 133 WorldCat member libraries worldwide
In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive L_2 \to L_q inequalities with respect to the Markov process given by the word length and with q an even integer. Interpolation and differentiation also yield general L_p \to L_q hypercontrativity for 1 <p \le q <\infty via logarithmic Sobolev inequalities. The authors' method admits further applications to ot
10 editions published between 2017 and 2018 in English and held by 133 WorldCat member libraries worldwide
In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive L_2 \to L_q inequalities with respect to the Markov process given by the word length and with q an even integer. Interpolation and differentiation also yield general L_p \to L_q hypercontrativity for 1 <p \le q <\infty via logarithmic Sobolev inequalities. The authors' method admits further applications to ot
H[lemniscate] functional calculus and square functions on noncommutative L[superscript p] spaces by
Marius Junge(
Book
)
3 editions published in 2006 in English and held by 30 WorldCat member libraries worldwide
3 editions published in 2006 in English and held by 30 WorldCat member libraries worldwide
Koordinatenfunktionen auf konvexen Körpern by
Marius Junge(
Book
)
2 editions published in 1991 in German and held by 10 WorldCat member libraries worldwide
2 editions published in 1991 in German and held by 10 WorldCat member libraries worldwide
Operator theory : the state of the art : conference proceedings, Timişoara, June 30  July 5, 2014 by International Conference on Operator Theory(
Book
)
2 editions published in 2016 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 2016 in English and held by 8 WorldCat member libraries worldwide
Factorization theory for spaces of operators by
Marius Junge(
Book
)
6 editions published between 1996 and 1999 in English and held by 7 WorldCat member libraries worldwide
6 editions published between 1996 and 1999 in English and held by 7 WorldCat member libraries worldwide
Rosenthal operator spaces(
Book
)
2 editions published in 2007 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2007 in English and held by 2 WorldCat member libraries worldwide
H¿h functional calculus and square functions on noncommutative Lpspaces by
Marius Junge(
Book
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
On poperator spaces and their applications by
Jung Jin Lee(
)
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
There have been a lot of research done on the relationship between locally compact groups and algebras associated with them. For example, Johnson proved that a locally compact group G is amenable if and only if the convolution algebra L1(G) is amenable as a Banach algebra, and Ruan showed that G is amenable if and only if the Fourier algebra A(G) of G is operator amenable. Motivated by Ruan's work, we want to study G through tools from poperator spaces. We _rst introduce the poperator space and various poperator space tensor products. We then study poperator space approximation property and poperator space completely bounded approximation property which are related to poperator space injective tensor product. We then apply these properties to the study of the pseudofunction algebra PFp(G), the pseudomeasure algebra PMp(G), and the Fig_aTalamancaHerz Algebra Ap(G). Especially we show that if G is discrete, the most of approximation properties for the reduced group C_algebra C_ _(G), the group von Neumann algebra V N(G), and the Fourier algebra A(G) (related to amenability, weak amenability, and approximation property of G) have natural panalogues for PFp(G), PMp(G), and Ap(G). With help of Herz's work, we also study the stability of these properties. Finally we discuss the properties Cp, C0p, and C00p which are natural panalogues of properties C, C0, and C00
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
There have been a lot of research done on the relationship between locally compact groups and algebras associated with them. For example, Johnson proved that a locally compact group G is amenable if and only if the convolution algebra L1(G) is amenable as a Banach algebra, and Ruan showed that G is amenable if and only if the Fourier algebra A(G) of G is operator amenable. Motivated by Ruan's work, we want to study G through tools from poperator spaces. We _rst introduce the poperator space and various poperator space tensor products. We then study poperator space approximation property and poperator space completely bounded approximation property which are related to poperator space injective tensor product. We then apply these properties to the study of the pseudofunction algebra PFp(G), the pseudomeasure algebra PMp(G), and the Fig_aTalamancaHerz Algebra Ap(G). Especially we show that if G is discrete, the most of approximation properties for the reduced group C_algebra C_ _(G), the group von Neumann algebra V N(G), and the Fourier algebra A(G) (related to amenability, weak amenability, and approximation property of G) have natural panalogues for PFp(G), PMp(G), and Ap(G). With help of Herz's work, we also study the stability of these properties. Finally we discuss the properties Cp, C0p, and C00p which are natural panalogues of properties C, C0, and C00
Noncommutative Lpspaces associated with locally compact quantum groups by
Thomas J Cooney(
)
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
[H^\infty] functional calculus and square functions on noncommutative [L^p]spaces(
Book
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
Nonstandard techniques in lifting theory by Jesse E Miller(
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
In this dissertation, a nonstandard approach to lifting theory developed by Bliedtner and Loeb is applied to liftings on topological measure spaces and group measure spaces. A further application to disintegrations of measures is given
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
In this dissertation, a nonstandard approach to lifting theory developed by Bliedtner and Loeb is applied to liftings on topological measure spaces and group measure spaces. A further application to disintegrations of measures is given
Embeddings of noncommutative Lpspaces in noncommutative L1spaces, 1<p<2(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
H [sup] [infinity] functional calculus and square functions on noncommutative L [sup] pspaces by
Marius Junge(
Book
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Gaussianlike von Neumann algebras and noncommutative brownian motion by Stephen Avsec(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
Efficient and guaranteed algorithms for sparse inverse problems by Kiryung Lee(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
Global dynamics of Schrodinger and Dirac equations by Ebru Toprak(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
In this document, we study the linear Schr\"odinger operator and linear massive Dirac operator in the $L^1\to L^\infty$ settings. In Chapter~I, we focus on the two dimensional Schr\"odinger operator in the weighted $L^1(\R^2) \rightarrow L^{\infty}(\R^2)$ setting when there is a resonance of the first kind at zero energy. In particular, we show that if $V(x)\les \la x \ra ^{4}$ and there is only swave resonance at zero of $H$, then $$ \big\ w^{1} \big( e^{itH}P_{ac} f  {\f 1 {\pi it} } F f \big) \big\ _{\infty} \leq \frac {C} {t (\logt)^2 } \wf\_1,\,\,\,\,\,\,t>2,$$ with $w(x)=\log^2(2+x)$. Here $Ff={\f 14} \psi\la \psi,f \ra$, where $\psi$ is an swave resonance function. We also extend this result to matrix Schr\"odinger equations with potentials under similar conditions. In Chapter~II, we focus on the two and three dimensional massive Dirac equation with a potential. In two dimension, we show that the $t^{1}$ decay rate holds if the threshold energies are regular or if there are swave resonances at the threshold. We further show that, if the threshold energies are regular then a faster decay rate of $t^{1}(\log t)^{2}$ is attained for large $t$, at the cost of logarithmic spatial weights, which is not the case for the free Dirac equation. In three dimension, we show that the solution operator is composed of a finite rank operator that decays at the rate $t^{1/2}$ plus a term that decays at the rate $t^{3/2}$
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
In this document, we study the linear Schr\"odinger operator and linear massive Dirac operator in the $L^1\to L^\infty$ settings. In Chapter~I, we focus on the two dimensional Schr\"odinger operator in the weighted $L^1(\R^2) \rightarrow L^{\infty}(\R^2)$ setting when there is a resonance of the first kind at zero energy. In particular, we show that if $V(x)\les \la x \ra ^{4}$ and there is only swave resonance at zero of $H$, then $$ \big\ w^{1} \big( e^{itH}P_{ac} f  {\f 1 {\pi it} } F f \big) \big\ _{\infty} \leq \frac {C} {t (\logt)^2 } \wf\_1,\,\,\,\,\,\,t>2,$$ with $w(x)=\log^2(2+x)$. Here $Ff={\f 14} \psi\la \psi,f \ra$, where $\psi$ is an swave resonance function. We also extend this result to matrix Schr\"odinger equations with potentials under similar conditions. In Chapter~II, we focus on the two and three dimensional massive Dirac equation with a potential. In two dimension, we show that the $t^{1}$ decay rate holds if the threshold energies are regular or if there are swave resonances at the threshold. We further show that, if the threshold energies are regular then a faster decay rate of $t^{1}(\log t)^{2}$ is attained for large $t$, at the cost of logarithmic spatial weights, which is not the case for the free Dirac equation. In three dimension, we show that the solution operator is composed of a finite rank operator that decays at the rate $t^{1/2}$ plus a term that decays at the rate $t^{3/2}$
Embeddings of oncommutative $ L _ p $spaces in noncommutative $ L _ 1 $spaces, 1 <p< 2 by
Marius Junge(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Parcet, Javier 1975 Opponent
 Perrin, Mathilde
 Société mathématique de France
 Le Merdy, Christian Opponent Thesis advisor
 Xu, Quanhua Opponent Thesis advisor
 Palazuelos, Carlos 1979
 Centre national de la recherche scientifique (France)
 American Mathematical Society Publisher
 Timotin, D. (Dan) 1953 Editor
 Vasilescu, FlorianHoria 1941 Editor