NDLI: Classes of Operator-Smooth Functions - II. Operator-Differentiable Functions

Content Provider	Springer Nature Link
Author	Kissin, E. Shulman, V.S.
Copyright Year	2004
Abstract	This paper studies the spaces of Gateaux and Frechet Operator Differentiable functions of a real variable and their link with the space of Operator Lipschitz functions. Apart from the standard operator norm on B(H), we consider a rich variety of spaces of Operator Differentiable and Operator Lipschitz functions with respect to symmetric operator norms. Our approach is aimed at the investigation of the interrelation and hierarchy of these spaces and of the intrinsic properties of Operator Differentiable functions. We apply the obtained results to the study of the functions acting on the domains of closed -derivations of C-algebras and prove that Operator Differentiable functions act on all such domains.We also obtain the following modification of this result: any continuously differentiable, Operator Lipschitz function acts on the domains of all weakly closed -derivations of C-algebras.
Ending Page	210
Page Count	46
Starting Page	165
File Format	PDF
ISSN	0378620X
e-ISSN	14208989
Journal	Integral Equations and Operator Theory
Issue Number	2
Volume Number	49
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2004-01-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Operator Derivations, dissipations and positive semigroups in $C^$ -algebras derivations C-algebras functions Operator ideals differentiable Lipschitz
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Analysis

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