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operator lipschitz functions

Proceedings of the Edinburgh Mathematical Society (1)

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CLASSES OF OPERATOR-SMOOTH FUNCTIONS. I. OPERATOR-LIPSCHITZ FUNCTIONS
Edward Kissin, Victor S. Shulman
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Proceedings of the Edinburgh Mathematical Society / Volume 48 / Issue 1 / February 2005

Published online by Cambridge University Press:

15 February 2005, pp. 151-173
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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