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

2005 ◽  
Vol 48 (1) ◽  
pp. 175-197 ◽  
Author(s):  
Edward Kissin ◽  
Victor S. Shulman
Keyword(s):  
Lipschitz Functions ◽  
Subject Classification ◽  
Primary 47A56 ◽  
Smooth Functions ◽  
Operator Stable ◽  
Operator Lipschitz Functions

AbstractThis 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

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

2005 ◽  
Vol 48 (1) ◽  
pp. 151-173 ◽  
Author(s):  
Edward Kissin ◽  
Victor S. Shulman
Keyword(s):  
Symmetric Operator ◽  
Lipschitz Functions ◽  
Operator Norm ◽  
Primary 47A56 ◽  
Intrinsic Properties ◽  
Smooth Functions ◽  
Rich Variety ◽  
Secondary 47L20 ◽  
Operator Norms ◽  
Operator Lipschitz Functions

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. 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

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