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CLASSES OF OPERATOR-SMOOTH FUNCTIONS. I. OPERATOR-LIPSCHITZ FUNCTIONS

Published online by Cambridge University Press:  15 February 2005

Edward Kissin  and
Victor S. Shulman
Edward Kissin
Affiliation:
Department of Computing, Communications Technology and Mathematics, London Metropolitan University, 166–220 Holloway Road, London N7 8DB, UK (e.kissin@londonmet.ac.uk)
Victor S. Shulman
Affiliation:
Department of Computing, Communications Technology and Mathematics, London Metropolitan University, 166–220 Holloway Road, London N7 8DB, UK (e.kissin@londonmet.ac.uk) Department of Mathematics, Vologda State Technical University, Vologda, Russia (shulman_v@yahoo.com)
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Abstract

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In 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. Our approach is aimed at the investigation of the interrelation and hierarchy of these spaces and of the intrinsic properties of operator-Lipschitz functions.

AMS 2000 Mathematics subject classification: Primary 47A56. Secondary 47L20

Keywords

operator Lipschitz functionssymmetrically normed ideals
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 1 , February 2005 , pp. 151 - 173
Copyright
Copyright © Edinburgh Mathematical Society 2005