Results 1 to 10 of about 166 (106)
Classes of Operator-Smooth Functions. I. Operator-Lipschitz Functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 2005 AbstractIn this paper we study the spaces of operator-Lipschitz functions and the spaces of functions closed to them: commutator bounded. Apart from the standard operator norm on $B(H)$, we consider a rich variety of symmetric operator norms and spaces of operator-Lipschitz functions with respect to these norms.
Edward Kissin, Víctor S Shulman
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On Lipschitz Functions of Normal Operators [PDF]
Proceedings of the American Mathematical Society, 1985 It is shown that if N N and ...
Fuad Kittaneh
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Krein’s Trace Formula for Unitary Operators and Operator Lipschitz Functions [PDF]
Functional Analysis and Its Applications, 2016 13 pages, in ...
Alexei Borisovich Aleksandrov +1 more
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On Fully Operator Lipschitz Functions
Journal of Functional Analysis, 2007 Let \(A(D)\) be the disk algebra of all continuous complex-valued functions on the unit disk \(D\) holomorphic in its interior. Functions from \(A(D)\) act on the set of all contraction operators on a Hilbert space. It is proved that the following classes of functions from \(A(D)\) coincide: (1)~the class of operator Lipschitz functions on the unit ...
Kissin, E., Shulman, V.S.
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Operator-Lipschitz functions in Schatten–von Neumann classes
Acta Mathematica, 2011 This paper resolves a number of conjectures in the perturbation theory of linear operators. Namely, we prove that every Lipschitz function is operator Lipschitz in the Schatten-von Neumann ideals $S^α$, $1 < α< \infty$. The negative result for $S^α$, $α= 1, \infty$ was earlier established by Yu. Farforovskaya in 1972.
Fedor Sukochev, Denis Potapov
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Lipschitz Estimates for Functions of Dirac and Schrödinger Operators
Journal of Mathematical Physics, 2021 We establish new Lipschitz-type bounds for functions of operators with noncompact perturbations that produce Schatten class resolvent differences. The results apply to suitable perturbations of Dirac and Schrödinger operators, including some long-range and random potentials, and to important classes of test functions. The key feature of these bounds is
Anna Skripka
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Notes on Pseudodifferential Operators Commutators and Lipschitz Functions
Open Mathematics, 2023 Abstract This article focuses on the boundedness of the commutators generated by pseudodifferential operators with Lipschitz functions and obtains a sufficient condition such that these operators are bounded from
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Hermitian Operators on Banach Algebras of Lipschitz Functions [PDF]
Proceedings of the American Mathematical Society, 2014 For compact metric spaces (X,d), we show that the Lipschitz spaces Lip(X,d) and the little Lipschitz spaces lip(X,d^α) with 0 < α < 1, equipped with the sum norm, support only trivial hermitian operators, that is, real multiples of the identity operator.
Jiménez Vargas, Antonio +2 more
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Lattice Lipschitz Superposition Operators on Banach Function Spaces
Journal of Mathematical Analysis and ApplicationsWe analyse and characterise the notion of lattice Lipschitz operator (a class of superposition operators, diagonal Lipschitz maps) when defined between Banach function spaces. After showing some general results, we restrict our attention to the case of those Lipschitz operators which are representable by pointwise composition with a strongly measurable
José M Calabuig +2 more
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Alexandria Engineering Journal, 2023 In this work, to show the existence and uniqueness solution of functional integrodifferential equation with nonlocal condition and finite delay function.
Kottakkaran Sooppy Nisar +2 more
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