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2 results

  • CLASSES OF OPERATOR-SMOOTH FUNCTIONS. III. STABLE FUNCTIONS AND FUGLEDE IDEALS

  • Edward Kissin, Victor S. Shulman
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 48 / Issue 1 / February 2005
    Published online by Cambridge University Press:
    15 February 2005, pp. 175-197
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  • This paper continue to study the interrelation and hierarchy of the spaces of operator-Lipschitz functions and the spaces of functions closed to them: commutator bounded and operator stable. It also examines various properties of symmetrically normed ideals, introduces new classes of ideals: regular and Fuglede, and investigates them.

    AMS 2000 Mathematics subject classification: Primary 47A56; 47L20

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

  • Edward Kissin, Victor S. Shulman
  • Journal:
    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