Dr Denis Potapov

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Research interests: ��Noncommutative analysis and noncommutative integration; perturbation theory; noncommutative and vector-valued harmonic analysis.

Best publications: ��(i) Operator-Lipschitz functions in Schatten-von Neumann classes --- Acta Math. (ii) Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators --- Adv. Math. (iii) Unbounded Fredholm modules and double operator integrals --- Crelle J.

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Phone

9385 7003

E-mail

d (dot) potapov (at) unsw (dot) edu (dot) au

Location

School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre East Wing, Room 6111

Book Chapters | 2019

Potapov D; Sukochev F; Vella D; Zanin D, 2019, 'A residue formula for locally compact noncommutative manifolds', in Positivity and Noncommutative Analysis, pp. 471 - 510,
Journal articles | 2024

Potapov D; Sukochev F; Zhou D, 2024, 'Noncommutative Nest Hardy Spaces and Martingales', International Mathematics Research Notices, 2024, pp. 13724 - 13757,

Journal articles | 2022

Carey A; Levitina G; Potapov D; Sukochev F, 2022, 'The Witten index and the spectral shift function', Reviews in Mathematical Physics, 34,

Journal articles | 2019

Aleksandrov AB; Peller VV; Potapov DS, 2019, 'On a Trace Formula for Functions of Noncommuting Operators', Mathematical Notes, 106, pp. 481 - 487,

Journal articles | 2019

Aleksandrov AB; Peller VV; Potapov DS, 2019, 'О формуле следов для функций от некоммутирующих операторов', Математические заметки, 106, pp. 483 - 490,

Journal articles | 2019

Caspers M; Potapov D; Sukochev F; Zanin D, 2019, 'WEAK TYPE COMMUTATOR AND LIPSCHITZ ESTIMATES: RESOLUTION OF THE NAZAROV-PELLER CONJECTURE', AMERICAN JOURNAL OF MATHEMATICS, 141, pp. 593 - 610,

Journal articles | 2019

Potapov D; Sukochev F; Tomskova A; Zanin D, 2019, 'FrÉchet differentiability of the norm of Lp-spaces associated with arbitrary von Neumann algebras', Transactions of the American Mathematical Society, 371, pp. 7493 - 7532,

Journal articles | 2018

Carey A; Gesztesy F; Kaad J; Levitina G; Nichols R; Potapov D; Sukochev F, 2018, 'On the Global Limiting Absorption Principle for Massless Dirac Operators', Annales Henri Poincare, 19, pp. 1993 - 2019,

Journal articles | 2017

Carey A; Gesztesy F; Potapov D; Sukochev F; Tomilov Y, 2017, 'On the Witten index in terms of spectral shift functions', Journal d'Analyse Mathematique, 132, pp. 1 - 61,

Journal articles | 2017

Potapov D; Skripka A; Sukochev F; Tomskova A, 2017, 'Multilinear Schur multipliers and Schatten properties of operator Taylor remainders', Advances in Mathematics, 320, pp. 1063 - 1098,

Journal articles | 2016

Carey A; Gesztesy F; Grosse H; Levitina G; Potapov D; Sukochev F; Zanin D, 2016, 'Trace formulas for a class of non-Fredholm operators: A review', Reviews in Mathematical Physics, 28,

Journal articles | 2016

Carey A; Gesztesy F; Levitina G; Nichols R; Potapov D; Sukochev F, 2016, 'Double operator integral methods applied to continuity of spectral shift functions', Journal of Spectral Theory, 6, pp. 747 - 779,

Journal articles | 2016

Carey A; Gesztesy F; Levitina G; Potapov D; Sukochev F; Zanin D, 2016, 'On index theory for non-Fredholm operators: A (1 + 1)-dimensional example', Mathematische Nachrichten, 289, pp. 575 - 609,

Journal articles | 2016

Coine C; Le Merdy C; Potapov D; Sukochev F; Tomskova A, 2016, 'Peller's problem concerning Koplienko–Neidhardt trace formulae: the unitary case', Journal of Functional Analysis, 271, pp. 1747 - 1763,

Journal articles | 2016

Coine C; Le Merdy C; Potapov D; Sukochev F; Tomskova A, 2016, 'Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae', Proceedings of the London Mathematical Society, 113, pp. 113 - 139,

Journal articles | 2016

Potapov D; Skripka A; Sukochev F, 2016, 'Functions of unitary operators: Derivatives and trace formulas', Journal of Functional Analysis, 270, pp. 2048 - 2072,

Journal articles | 2015

Caspers M; Potapov D; Sukochev F; Zanin D, 2015, 'Weak type estimates for the absolute value mapping', Journal of Operator Theory, 73, pp. 361 - 384,

Journal articles | 2015

Potapov D; Skripka A; Sukochev F, 2015, 'Trace formulas for resolvent comparable operators', Advances in Mathematics, 272, pp. 630 - 651,

Journal articles | 2015

Potapov D; Sukochev F; Tomskova A, 2015, 'On the Arazy conjecture concerning Schur multipliers on Schatten ideals', Advances in Mathematics, 268, pp. 404 - 422,

Journal articles | 2015

Potapov D; Sukochev F; Usachev A; Zanin D, 2015, 'Singular traces and perturbation formulae of higher order', Journal of Functional Analysis, 269, pp. 1441 - 1481,

Journal articles | 2014

Carey A; Gesztesy F; Potapov D; Sukochev F; Tomilov Y, 2014, 'A Jost-Pais-Type Reduction of Fredholm Determinants and Some Applications', Integral Equations and Operator Theory, 79, pp. 389 - 447,

Journal articles | 2014

Caspers M; Montgomery-Smith S; Potapov D; Sukochev F, 2014, 'The best constants for operator Lipschitz functions on Schatten classes', Journal of Functional Analysis, 267, pp. 3557 - 3579,

Journal articles | 2014

Potapov D; Skripka A; Sukochev F, 2014, 'Functions of unitary operators: Derivatives and trace formulas', Journal of Functional Analysis,

Journal articles | 2014

Potapov D; Skripka A; Sukochev F, 2014, 'Higher-order spectral shift for contractions', Proceedings of the London Mathematical Society, 108, pp. 327 - 349,

Journal articles | 2014

Potapov D; Sukochev F; Tomskova A; Zanin D, 2014, 'Fréchet differentiability of the norm of Lp-spaces associated with arbitrary von Neumann algebras', Comptes Rendus Mathematique, 352, pp. 923 - 927,

Journal articles | 2014

Potapov D; Sukochev F; Zanin D, 2014, 'Krein's trace theorem revisited', Journal of Spectral Theory, 4, pp. 415 - 430,

Journal articles | 2014

Potapov D; Sukochev F, 2014, 'Fréchet differentiability of S^p norms', Advances in Mathematics, 262, pp. 436 - 475,

Journal articles | 2013

Caspers ; Potapov D; Sukochev F, 2013, 'The Walsh basis in the Lp-spaces of hyperfinite IIIλ factors, 0', Journal of Mathematical Analysis and Applications, 408, pp. 154 - 164,

Journal articles | 2013

Kalton N; Lord S; Potapov D; Sukochev F, 2013, 'Traces of compact operators and the noncommutative residue', Advances in Mathematics, 235, pp. 1 - 55,

Journal articles | 2013

Potapov D; Skripka A; Sukochev F, 2013, 'On Hilbert-Schmidt compatibility', Operators and Matrices, 7, pp. 1 - 33,

Journal articles | 2013

Potapov D; Skripka A; Sukochev F, 2013, 'Spectral shift function of higher order', Inventiones Mathematicae, 193, pp. 501 - 538,

Journal articles | 2012

Kissin EV; Potapov DS; Shulman VS; Sukochev FA, 2012, 'Operator smoothness in Schatten norms for functions of several variables: Lipschitz conditions, differentiability and unbounded derivations', Proceedings of the London Mathematical Society, 3rd Series, 105, pp. 661 - 702,

Journal articles | 2012

Potapov D; Sukochev F; Xu Q, 2012, 'On the vector-valued Littlewood-Paley-Rubio de Francia inequality', Revista Matematica Iberoamericana, 28, pp. 839 - 856,

Journal articles | 2012

Potapov D; Sukochev F, 2012, 'Koplienko Spectral Shift Function on the Unit Circle', Communications in Mathematical Physics, 309, pp. 693 - 702,

Journal articles | 2011

Aleksandrov A; Peller V; Potapov D; Sukochev F, 2011, 'Functions of normal operators under perturbations', Advances in Mathematics, 226, pp. 5216 - 5251,

Journal articles | 2011

Dirksen S; De Pagter B; Potapov D; Sukochev F, 2011, 'Rosenthal inequalities in noncommutative symmetric spaces', Journal of Functional Analysis, 261, pp. 2890 - 2925,

Journal articles | 2011

Kissin E; Potapov D; Shulman V; Sukochev F, 2011, 'Lipschitz functions, Schatten ideals, and unbounded derivations', Functional Analysis and Its Applications, 45, pp. 157 - 159

Journal articles | 2011

Potapov D; Sukochev F, 2011, 'Operator-Lipschitz functions in Schatten-von Neumann classes', ACTA Mathematica, 207, pp. 375 - 389,

Journal articles | 2011

Potapov D; Sukochev F, 2011, 'The Haar system in the preduals of hyperfinite factors', Canadian Mathematical Bulletin, 54, pp. 347 - 363,

Journal articles | 2010

Aleksandrov A; Peller V; Potapov D; Sukochev F, 2010, 'Functions of perturbed normal operators', Comptes Rendus Mathematique, 348, pp. 553 - 558,

Journal articles | 2010

Lord S; Potapov D; Sukochev F, 2010, 'Measures from Dixmier traces and zeta functions', Journal of Functional Analysis, 259, pp. 1915 - 1949,

Journal articles | 2010

Potapov D; Sukochev F, 2010, 'Double operator integrals and submajorization', Mathematical Modelling of Natural Phenomena (MMNP), 5, pp. 317 - 339,

Journal articles | 2009

Carey AL; Potapov D; Sukochev F, 2009, 'Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators', Advances in Mathematics, 222, pp. 1809 - 1849

Journal articles | 2009

Potapov D; Sukochev F, 2009, 'Unbounded Fredholm modules and double operator integrals', Journal fur die Reine und Angewandte Mathematik, pp. 159 - 185,

Journal articles | 2009

Potapov D; Sukochev F, 2009, 'Unbounded Fredholm modules and double operator integrals', Journal fur die Reine und Angewandte Mathematik, 626, pp. 159 - 185,

Journal articles | 2008

Potapov D; Sukochev F, 2008, 'Lipschitz and commutator estimates in symmetric operator spaces', Journal of Operator Theory, 59, pp. 211 - 234

Journal articles | 2007

Potapov D; Sukochev F, 2007, 'Non-(quantum) differentiable C1-functions in the spaces with trivial Boyd indices', Integral Equations and Operator Theory, 57, pp. 247 - 261

Journal articles | 2006

Potapov D; Hytonen TP, 2006, 'Vector-valued multiplier theorems of Coifman-Rubio de Francia-Semmes type', Archiv der Mathematik, 87, pp. 245 - 254,

Journal articles | 2005

Sukochev F; Potapov D, 2005, 'A vector-valued Littlewood-Paley theorem for an arbitrary set of intervals and its applications', Comptes Rendus de l`Academie des Sciences de L Urss, 404, pp. 598 - 600
Preprints | 2021

Carey A; Levitina G; Potapov D; Sukochev F, 2021, The Witten index and the spectral shift function, ,

Preprints | 2019

Aleksandrov AB; Peller VV; Potapov DS, 2019, On a trace formula for functions of noncommuting operators, ,

Preprints | 2017

Carey A; Gesztesy F; Kaad J; Levitina G; Nichols R; Potapov D; Sukochev F, 2017, On the Global Limiting Absorption Principle for Massless Dirac Operators, ,

Preprints | 2016

Carey A; Gesztesy F; Grosse H; Levitina G; Potapov D; Sukochev F; Zanin D, 2016, Trace Formulas for a Class of non-Fredholm Operators: A Review, ,

Preprints | 2016

Potapov D; Sukochev F; Usachev A; Zanin D, 2016, Singular traces and perturbation formulae of higher order, ,

Preprints | 2015

Carey A; Gesztesy F; Levitina G; Nichols R; Potapov D; Sukochev F, 2015, Double operator integral methods applied to continuity of spectral shift functions, ,

Preprints | 2015

Carey A; Gesztesy F; Levitina G; Potapov D; Sukochev F; Zanin D, 2015, On Index Theory for Non-Fredholm Operators: A $(1+1)$-Dimensional Example, ,

Preprints | 2015

Caspers M; Potapov D; Sukochev F; Zanin D, 2015, Weak type commutator and Lipschitz estimates: resolution of the Nazarov-Peller conjecture, ,

Preprints | 2015

Coine C; Merdy CL; Potapov D; Sukochev F; Tomskova A, 2015, Peller's problem concerning Koplienko-Neidhardt trace formulae: the unitary case, ,

Preprints | 2015

Coine C; Merdy CL; Potapov D; Sukochev F; Tomskova A, 2015, Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae, ,

Preprints | 2014

Carey A; Gesztesy F; Potapov D; Sukochev F; Tomilov Y, 2014, A Jost-Pais-type reduction of Fredholm determinants and some applications, ,

Preprints | 2014

Carey A; Gesztesy F; Potapov D; Sukochev F; Tomilov Y, 2014, On the Witten index in terms of spectral shift functions, ,

Preprints | 2013

Caspers M; Potapov D; Sukochev F; Zanin D, 2013, Weak type estimates for the absolute value mapping, ,

Preprints | 2012

Caspers M; Montgomery-Smith S; Potapov D; Sukochev F, 2012, The best constants for operator Lipschitz functions on Schatten classes, ,

Preprints | 2012

Kalton N; Lord S; Potapov D; Sukochev F, 2012, Traces of compact operators and the noncommutative residue, ,

Preprints | 2012

Potapov D; Skripka A; Sukochev F, 2012, Higher order spectral shift for contractions, ,

Preprints | 2011

Caspers M; Potapov D; Sukochev F, 2011, The Walsh basis in the Lp-spaces of hyperfinite III_\lambda-factors, 0 < \lambda <= 1, ,

Preprints | 2010

Aleksandrov A; Peller V; Potapov D; Sukochev F, 2010, Functions of normal operators under perturbations, ,

Preprints | 2010

Aleksandrov A; Peller V; Potapov D; Sukochev F, 2010, Functions of perturbed normal operators, ,

Preprints | 2009

Potapov D; Skripka A; Sukochev F, 2009, Spectral shift function of higher order, ,

Preprints | 2008

Carey A; Potapov D; Sukochev F, 2008, Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators, ,

Preprints | 2008

Potapov D; Sukochev F, 2008, Non- (quantum) differentiable $C^1$-functions in the spaces with trivial Boyd indices, ,

Preprints | 2008

Potapov D; Sukochev F, 2008, The Haar system in the preduals of hyperfinite factors, ,

Preprints | 2008

Potapov D; Sukochev F, 2008, Unbounded Fredholm modules and double operator integrals, ,

Conference Papers | 2007

Potapov D, 2007, 'Commutator estimates in the operator Lp-spaces', in Proceedings of the Centre for Mathematics and its applications, Centre for Mathematics and its applications, presented at Centre for Mathematics and its applications

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