Denis Potapov - Academia.edu (original) (raw)

Papers by Denis Potapov

Research paper thumbnail of Functions of unitary operators: Derivatives and trace formulas

Journal of Functional Analysis, 2016

Research paper thumbnail of Unbounded Fredholm modules and double operator integrals

J Reine Angew Math, 2009

In noncommutative geometry one is interested in invariants such as the Fredholm index or spectral... more In noncommutative geometry one is interested in invariants such as the Fredholm index or spectral flow and their calculation using cyclic cocycles. A variety of formulae have been established under side conditions called summability constraints. These can be formulated in two ways, either for spectral triples or for bounded Fredholm modules. We study the relationship between these by proving various properties of the map on unbounded self adjoint operators DDD given by f(D)=D(1+D2)−1/2f(D)=D(1+D^2)^{-1/2}f(D)=D(1+D2)−1/2. In particular we prove commutator estimates which are needed for the bounded case. In fact our methods work in the setting of semifinite noncommutative geometry where one has DDD as an unbounded self adjoint linear operator affiliated with a semi-finite von Neumann algebra aM\aMaM. More precisely we show that for a pair D,D0D,D_0D,D0 of such operators with D−D0D-D_0D−D0 a bounded self-adjoint linear operator from aM\aMaM and $ ({\bf 1}+D_0^2)^{-1/2}\in \sE$, where sE\sEsE is a noncommutative symmetric space associated with aM\aMaM, then Vertf(D)−f(D0)VertsEleqCcdotVertD−D0VertaM.\Vert f(D) - f (D_0) \Vert_{\sE} \leq C\cdot \Vert D-D_0\Vert_{\aM}.Vertf(D)−f(D0)VertsEleqCcdotVertD−D0VertaM. This result is further used to show continuous differentiability of the mapping between an odd sE\sEsE-summable spectral triple and its bounded counterpart.

Research paper thumbnail of On index theory for non-Fredholm operators: A (1 + 1)-dimensional example

Mathematische Nachrichten, 2015

Research paper thumbnail of Frechet differentiability of Sp norms

One of the long standing questions in the theory of Schatten-von Neumann ideals of compact operat... more One of the long standing questions in the theory of Schatten-von Neumann ideals of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts. We answer this question in the affirmative. A key technical observation underlying our proof is a discovery of connection between this question and recent affirmative resolution of L.S. Koplienko's conjecture concerning existence of higher order spectral shift functions.

Research paper thumbnail of The Haar System in the Preduals of Hyperfinite Factors

Canadian Mathematical Bulletin, 2011

We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types I... more We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types II1, II∞, III λ , 0 < λ ≤ 1. In the semifinite (respectively, purely infinite) setting, these systems form Schauder bases in any associated separable symmetric space of measurable operators (respectively, in any non-commutative L

Research paper thumbnail of Non- (Quantum) Differentiable C1-Functions in the Spaces with Trivial Boyd Indices

Integral Equation Oper Theory, 2007

If E is a separable symmetric sequence space with trivial Boyd indices and cCE\cC^EcCE is the corresp... more If E is a separable symmetric sequence space with trivial Boyd indices and cCE\cC^EcCE is the corresponding ideal of compact operators, then there exists a C1C^1C1-function fEf_EfE, a self-adjoint element WincCEW\in \cC^EWincCE and a densely defined closed symmetric derivation delta\deltadelta on cCE\cC^EcCE such that WinDomdeltaW \in Dom \deltaWinDomdelta, but fE(W)notinDomdeltaf_E(W) \notin Dom \deltafE(W)notinDomdelta.

Research paper thumbnail of Singular traces and perturbation formulae of higher order

Journal of Functional Analysis, 2015

Research paper thumbnail of Fréchet differentiability of the norm of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www...

Comptes Rendus Mathematique, 2014

Research paper thumbnail of Krein's trace theorem revisited

Journal of Spectral Theory, 2014

Research paper thumbnail of On the Witten index in terms of spectral shift functions

Dedicated with admiration to Sergio Albeverio on the occasion of his 75th birthday.

Research paper thumbnail of On the Arazy conjecture concerning Schur multipliers on Schatten ideals

Advances in Mathematics, 2015

Available online xxxx Communicated by Dan Voiculescu MSC: 47B10 47A13 Keywords: Schur multipliers... more Available online xxxx Communicated by Dan Voiculescu MSC: 47B10 47A13 Keywords: Schur multipliers Schatten ideals Double operator integral ∞ j,k=1

Research paper thumbnail of The best constants for operator Lipschitz functions on Schatten classes

Research paper thumbnail of The mechanism of allyl isomerization of unsaturated compounds catalyzed by organomagnesium clusters

Russian Journal of Physical Chemistry, 2006

The paper presents a density functional theory investigation of the mechanism of allyl isomerizat... more The paper presents a density functional theory investigation of the mechanism of allyl isomerization of olefins on magnesium clusters for the example of the Mg4-allylbenzene system. The rearrangement of the cluster compound corresponding to the insertion of the tetranuclear cluster at a C-H allylbenzene bond into a structure derivative from 2-methylstyrene is an activationless reaction. The limiting step is the liberation of the cluster nucleus capable of interacting with another allylbenzene molecule. Cluster decomposition competes with this process; this conclusion is in agreement with experimental short lifetimes of cluster magnesium hydride catalysts.

Research paper thumbnail of Catalytic isomerization of allylbenzene on organomagnesium clusters

Russian Chemical Bulletin, 2005

Catalytic isomerization of allylbenzene to form trans β methylstyrene quantitatively oc curs on t... more Catalytic isomerization of allylbenzene to form trans β methylstyrene quantitatively oc curs on the magnesium-anthracene cluster adduct under mild conditions. A low stability organomagnesium compound, presumably of the cluster nature and active in catalytic allylbenzene isomerization, is formed by cocondensation of magnesium and allylbenzene va pors at the liquid nitrogen temperature. The products of low temperature solid phase reactions of magnesium with hydrocarbons containing aromatic rings exhibit high catalytic activity in the allyl isomerization of allylbenzene.

Research paper thumbnail of On the vector-valued Littlewood–Paley–Rubio de Francia inequality

Revista Matemática Iberoamericana, 2012

The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LP Rp, ... more The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LP Rp, 2 ≤ p < ∞. The paper shows that every Banach lattice whose 2-concavification is a UMD Banach lattice has this property. The paper also shows that every space having LP Rq also has LP Rp with q ≤ p < ∞.

Research paper thumbnail of Higher-order spectral shift for contractions

Proceedings of the London Mathematical Society, 2014

Research paper thumbnail of Synthesis of Cluster Alkyl and Aryl Grignard Reagents in Solution

Organometallics, 2004

Cluster alkyl Grignard reagents, alkyltetramagnesium chlorides, have been obtained by exchange re... more Cluster alkyl Grignard reagents, alkyltetramagnesium chlorides, have been obtained by exchange reaction between phenyltetramagnesium fluoride and organic halides in excess halide solution at room temperature. Transmetalation between PhCl, PhBr, and phenyltetramagnesium fluoride with the formation of PhMg 4 X (X ) Cl, Br) has been shown to occur.

Research paper thumbnail of On Hilbert-Schmidt compatibility

Operators and Matrices, 2013

Research paper thumbnail of Double Operator Integrals and Submajorization

Mathematical Modelling of Natural Phenomena, 2010

Research paper thumbnail of Rosenthal inequalities in noncommutative symmetric spaces

Journal of Functional Analysis, 2011

We give a direct proof of the 'upper'Khintchine inequality for a noncommutative symmetric... more We give a direct proof of the 'upper'Khintchine inequality for a noncommutative symmetric (quasi-) Banach function space with nontrivial upper Boyd index. This settles an open question of C. Le Merdy and the fourth named author (Le Merdy and Sukochev, 2008 [24]) ...

Research paper thumbnail of Functions of unitary operators: Derivatives and trace formulas

Journal of Functional Analysis, 2016

Research paper thumbnail of Unbounded Fredholm modules and double operator integrals

J Reine Angew Math, 2009

In noncommutative geometry one is interested in invariants such as the Fredholm index or spectral... more In noncommutative geometry one is interested in invariants such as the Fredholm index or spectral flow and their calculation using cyclic cocycles. A variety of formulae have been established under side conditions called summability constraints. These can be formulated in two ways, either for spectral triples or for bounded Fredholm modules. We study the relationship between these by proving various properties of the map on unbounded self adjoint operators DDD given by f(D)=D(1+D2)−1/2f(D)=D(1+D^2)^{-1/2}f(D)=D(1+D2)−1/2. In particular we prove commutator estimates which are needed for the bounded case. In fact our methods work in the setting of semifinite noncommutative geometry where one has DDD as an unbounded self adjoint linear operator affiliated with a semi-finite von Neumann algebra aM\aMaM. More precisely we show that for a pair D,D0D,D_0D,D0 of such operators with D−D0D-D_0D−D0 a bounded self-adjoint linear operator from aM\aMaM and $ ({\bf 1}+D_0^2)^{-1/2}\in \sE$, where sE\sEsE is a noncommutative symmetric space associated with aM\aMaM, then Vertf(D)−f(D0)VertsEleqCcdotVertD−D0VertaM.\Vert f(D) - f (D_0) \Vert_{\sE} \leq C\cdot \Vert D-D_0\Vert_{\aM}.Vertf(D)−f(D0)VertsEleqCcdotVertD−D0VertaM. This result is further used to show continuous differentiability of the mapping between an odd sE\sEsE-summable spectral triple and its bounded counterpart.

Research paper thumbnail of On index theory for non-Fredholm operators: A (1 + 1)-dimensional example

Mathematische Nachrichten, 2015

Research paper thumbnail of Frechet differentiability of Sp norms

One of the long standing questions in the theory of Schatten-von Neumann ideals of compact operat... more One of the long standing questions in the theory of Schatten-von Neumann ideals of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts. We answer this question in the affirmative. A key technical observation underlying our proof is a discovery of connection between this question and recent affirmative resolution of L.S. Koplienko's conjecture concerning existence of higher order spectral shift functions.

Research paper thumbnail of The Haar System in the Preduals of Hyperfinite Factors

Canadian Mathematical Bulletin, 2011

We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types I... more We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types II1, II∞, III λ , 0 < λ ≤ 1. In the semifinite (respectively, purely infinite) setting, these systems form Schauder bases in any associated separable symmetric space of measurable operators (respectively, in any non-commutative L

Research paper thumbnail of Non- (Quantum) Differentiable C1-Functions in the Spaces with Trivial Boyd Indices

Integral Equation Oper Theory, 2007

If E is a separable symmetric sequence space with trivial Boyd indices and cCE\cC^EcCE is the corresp... more If E is a separable symmetric sequence space with trivial Boyd indices and cCE\cC^EcCE is the corresponding ideal of compact operators, then there exists a C1C^1C1-function fEf_EfE, a self-adjoint element WincCEW\in \cC^EWincCE and a densely defined closed symmetric derivation delta\deltadelta on cCE\cC^EcCE such that WinDomdeltaW \in Dom \deltaWinDomdelta, but fE(W)notinDomdeltaf_E(W) \notin Dom \deltafE(W)notinDomdelta.

Research paper thumbnail of Singular traces and perturbation formulae of higher order

Journal of Functional Analysis, 2015

Research paper thumbnail of Fréchet differentiability of the norm of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www...

Comptes Rendus Mathematique, 2014

Research paper thumbnail of Krein's trace theorem revisited

Journal of Spectral Theory, 2014

Research paper thumbnail of On the Witten index in terms of spectral shift functions

Dedicated with admiration to Sergio Albeverio on the occasion of his 75th birthday.

Research paper thumbnail of On the Arazy conjecture concerning Schur multipliers on Schatten ideals

Advances in Mathematics, 2015

Available online xxxx Communicated by Dan Voiculescu MSC: 47B10 47A13 Keywords: Schur multipliers... more Available online xxxx Communicated by Dan Voiculescu MSC: 47B10 47A13 Keywords: Schur multipliers Schatten ideals Double operator integral ∞ j,k=1

Research paper thumbnail of The best constants for operator Lipschitz functions on Schatten classes

Research paper thumbnail of The mechanism of allyl isomerization of unsaturated compounds catalyzed by organomagnesium clusters

Russian Journal of Physical Chemistry, 2006

The paper presents a density functional theory investigation of the mechanism of allyl isomerizat... more The paper presents a density functional theory investigation of the mechanism of allyl isomerization of olefins on magnesium clusters for the example of the Mg4-allylbenzene system. The rearrangement of the cluster compound corresponding to the insertion of the tetranuclear cluster at a C-H allylbenzene bond into a structure derivative from 2-methylstyrene is an activationless reaction. The limiting step is the liberation of the cluster nucleus capable of interacting with another allylbenzene molecule. Cluster decomposition competes with this process; this conclusion is in agreement with experimental short lifetimes of cluster magnesium hydride catalysts.

Research paper thumbnail of Catalytic isomerization of allylbenzene on organomagnesium clusters

Russian Chemical Bulletin, 2005

Catalytic isomerization of allylbenzene to form trans β methylstyrene quantitatively oc curs on t... more Catalytic isomerization of allylbenzene to form trans β methylstyrene quantitatively oc curs on the magnesium-anthracene cluster adduct under mild conditions. A low stability organomagnesium compound, presumably of the cluster nature and active in catalytic allylbenzene isomerization, is formed by cocondensation of magnesium and allylbenzene va pors at the liquid nitrogen temperature. The products of low temperature solid phase reactions of magnesium with hydrocarbons containing aromatic rings exhibit high catalytic activity in the allyl isomerization of allylbenzene.

Research paper thumbnail of On the vector-valued Littlewood–Paley–Rubio de Francia inequality

Revista Matemática Iberoamericana, 2012

The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LP Rp, ... more The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LP Rp, 2 ≤ p < ∞. The paper shows that every Banach lattice whose 2-concavification is a UMD Banach lattice has this property. The paper also shows that every space having LP Rq also has LP Rp with q ≤ p < ∞.

Research paper thumbnail of Higher-order spectral shift for contractions

Proceedings of the London Mathematical Society, 2014

Research paper thumbnail of Synthesis of Cluster Alkyl and Aryl Grignard Reagents in Solution

Organometallics, 2004

Cluster alkyl Grignard reagents, alkyltetramagnesium chlorides, have been obtained by exchange re... more Cluster alkyl Grignard reagents, alkyltetramagnesium chlorides, have been obtained by exchange reaction between phenyltetramagnesium fluoride and organic halides in excess halide solution at room temperature. Transmetalation between PhCl, PhBr, and phenyltetramagnesium fluoride with the formation of PhMg 4 X (X ) Cl, Br) has been shown to occur.

Research paper thumbnail of On Hilbert-Schmidt compatibility

Operators and Matrices, 2013

Research paper thumbnail of Double Operator Integrals and Submajorization

Mathematical Modelling of Natural Phenomena, 2010

Research paper thumbnail of Rosenthal inequalities in noncommutative symmetric spaces

Journal of Functional Analysis, 2011

We give a direct proof of the 'upper'Khintchine inequality for a noncommutative symmetric... more We give a direct proof of the 'upper'Khintchine inequality for a noncommutative symmetric (quasi-) Banach function space with nontrivial upper Boyd index. This settles an open question of C. Le Merdy and the fourth named author (Le Merdy and Sukochev, 2008 [24]) ...