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The Extended Field of Operator Theory pp 225–244Cite as

Extension of Operator Lipschitz and Commutator Bounded Functions

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 171))

Abstract

Let (B(H) ‖·‖) be the algebra of all bounded operators on an infinite-dimensional Hilbert space H. Let B(H)sa be the set of all selfadjoint operators in B(H). Throughout the paper we denote by α a compact subset of ℝ and by B(H)sa(α) the set of all operators in B(H)sa with spectrum in α:

$$ B(H)_{sa} (\alpha ) = \{ A = A^* \in B(H): Sp(A) \subseteq \alpha \} . $$

We will use similar notations A sa, A sa(α) for a Banach *-algebra A. Each bounded Borel function g on α defines, via the spectral theorem, a map A → g(A) from B(H)sa(α) into B(H). Various smoothness conditions when imposed on this map define the corresponding classes of operator-smooth functions.

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Author information

Authors and Affiliations

  1. Department of Computing, Communications Technology and Mathematics, London Metropolitan University, Holloway Road, London, N7 8DB, Great Britain

    Edward Kissin

  2. Department of Mathematics, Vologda State Technical University, Vologda, Russia

    Victor S. Shulman

  3. Department of Mathematics, Chalmers University of Technology, Gothenburg, Sweden

    Lyudmila B. Turowska

Authors
  1. Edward Kissin
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  2. Victor S. Shulman
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  3. Lyudmila B. Turowska
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK

    Michael A. Dritschel

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Kissin, E., Shulman, V.S., Turowska, L.B. (2006). Extension of Operator Lipschitz and Commutator Bounded Functions. In: Dritschel, M.A. (eds) The Extended Field of Operator Theory. Operator Theory: Advances and Applications, vol 171. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7980-3_11

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