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Просмотр по автору "Bikchentaev A."

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  • Ando's inequality for uniform submajorization 
    Bikchentaev A.; McDonald E.; Sukochev F. (2020)
    © 2020 Elsevier Inc. We discuss Ando's inequality involving operator monotone functions and demonstrate that a natural strengthening of Ando's result to uniform submajorization holds if and only if the operator monotone ...
  • Block projection operators in normed solid spaces of measurable operators 
    Bikchentaev A. (2012)
    We prove a Hermitian analog of the well-known operator triangle inequality for vonNeumann algebras. In the semifinite case we show that a block projection operator is a linear positive contraction on a wide class of solid ...
  • Characterization of the trace by monotonicity inequalities 
    Bikchentaev A.; Tikhonov O. (2007)
    Let φ{symbol}be a positive linear functional on the algebra of n × n complex matrices and p be a number greater than 1. The main result of the paper says that if for any pair A, B of positive semi-definite n × n matrices ...
  • Characterization of the trace by young's inequality 
    Bikchentaev A.; Tikhonov O. (2005)
    Let φ be a positive linear functional on the algebra of n × n complex matrices and p, q be positive numbers such that 1/p + 1/q = 1. We prove that if for any pair A, B of positive semi-definite n × n matrices the inequality ...
  • Commutation of Projections and Characterization of Traces on von Neumann Algebras. III 
    Bikchentaev A. (2015)
    © 2015, Springer Science+Business Media New York. We obtain new necessary and sufficient commutation conditions for nonnegative operators and projections in terms of operator inequalities. It is shown that in the general ...
  • Commutation of projections and trace characterization on von Neumann algebras. II 
    Bikchentaev A. (2011)
    We obtain new necessary and sufficient commutation conditions for projections in terms of operator inequalities. These inequalities are applied for trace characterization on von Neumann algebras for the class of all positive ...
  • Commutativity of projections and characterization of traces on Von Neumann algebras 
    Bikchentaev A. (2010)
    We find new necessary and sufficient conditions for the commutativity of projections in terms of operator inequalities. We apply these inequalities to characterize a trace on von Neumann algebras in the class of all positive ...
  • Concerning the theory of τ-measurable operators affiliated to a semifinite von Neumann algebra 
    Bikchentaev A. (2015)
    © 2015, Pleiades Publishing, Ltd. Let M be a von Neumann algebra of operators in a Hilbert space H, let τ be an exact normal semifinite trace on M, and let L1(M, τ) be the Banach space of τ-integrable operators. The following ...
  • Convergence of integrable operators affiliated to a finite von Neumann algebra 
    Bikchentaev A. (2016)
    © 2016, Pleiades Publishing, Ltd.In the Banach space L1(M, τ) of operators integrable with respect to a tracial state τ on a von Neumann algebra M, convergence is analyzed. A notion of dispersion of operators in L2(M, τ) ...
  • Differences of idempotents in C*-algebras 
    Bikchentaev A. (2017)
    © 2017, Pleiades Publishing, Ltd.Suppose that P and Q are idempotents on a Hilbert space H, while Q = Q* and I is the identity operator in H. If U = P − Q is an isometry then U = U* is unitary and Q = I − P. We establish ...
  • Dominated convergence in measure on semifinite von Neumann algebras and arithmetic averages of measurable operators 
    Bikchentaev A.; Sabirova A. (2012)
    Consider a von Neumann algebra M with a faithful normal semifinite trace τ. We prove that each order bounded sequence of τ-compact operators includes a subsequence whose arithmetic averages converge in τ. We also prove a ...
  • Foreword 
    Bikchentaev A.; Rad S.R.; Turilova E. (2021)
  • Ideal F-norms on C*-algebras 
    Bikchentaev A. (2015)
    © 2015, Allerton Press, Inc. We show that every measure of non-compactness on a W*-algebra is an ideal F-pseudonorm. We establish a criterion of the right Fredholm property of an element with respect to a W*-algebra. We ...
  • Ideal F-Norms on C*-Algebras. II 
    Bikchentaev A. (2019)
    © 2019, Allerton Press, Inc. We study ideal F-norms ‖·‖p, 0 <p < +∞ associated with a trace ϕ on a C*-algebra A. If A, B of A are such that |A|≤ |B|,then ‖A‖p ≤ ‖B‖p. We have ‖A‖p = ‖A*‖p for all A from A (0 <p < +∞)and a ...
  • Inequalities for the block projection operators 
    Bikchentaev A.; Sukochev F. (2021)
    Originally studied by Gohberg and Krein, the block projection operators admit a natural extension to the setting of quasi-normed ideals and noncommutative integration. Here, we establish several uniform submajorization ...
  • Inequality for a trace on a unital C*-algebra 
    Bikchentaev A. (2016)
    © 2016, Pleiades Publishing, Ltd.A new inequality for a trace on a unital C*-algebra is established. It is shown that the inequality obtained characterizes the traces in the class of all positive functionals on a unital ...
  • Integrable products of measurable operators 
    Bikchentaev A. (2016)
    © 2016, Pleiades Publishing, Ltd.Let τ be a faithful normal semifinite trace on von Neumann algebra M, 0 < p < +∞ and Lp(M, τ) be the space of all integrable (with respect to τ) with degree p operators, assume also that M ...
  • Local convergence in measure on semifinite von Neumann algebras 
    Bikchentaev A. (2006)
    Suppose that M is a von Neumann algebra of operators on a Hilbert space H and τ is a faithful normal semifinite trace on M. The set M̃ of all τ-measurable operators with the topology tτ of convergence in measure is a ...
  • Majorization for products of measurable operators 
    Bikchentaev A. (1998)
    A new equality for a faithful normal semifinite trace on a von Neumann algebra is proved. We conjecture a strengthening of the result.
  • Minimality of convergence in measure topologies on finite von Neumann algebras 
    Bikchentaev A. (2004)
    We prove that the natural embedding of the metric ideal space on a finite von Neumann algebra M into the *-algebra of measurable operators M̃ endowed with the topology of convergence in measure is continuous. Using this ...

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