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A KADISON–SAKAI-TYPE THEOREM

Part of: Selfadjoint operator algebras Special classes of linear operators

Published online by Cambridge University Press:  13 March 2009

MADJID MIRZAVAZIRI  and
MOHAMMAD SAL MOSLEHIAN
MADJID MIRZAVAZIRI
Affiliation:
Department of Mathematics, Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran Banach Mathematical Research Group (BMRG), Mashhad, Iran (email: mirzavaziri@math.um.ac.ir) Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Iran (email: madjid@mirzavaziri.com)
MOHAMMAD SAL MOSLEHIAN*
Affiliation:
Department of Mathematics, Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran (email: moslehian@ferdowsi.um.ac.ir) Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Iran (email: moslehian@ams.org)
*
✉For correspondence; e-mail: moslehian@ferdowsi.um.ac.ir, moslehian@ams.org
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Abstract

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Suppose that σ:𝔐→𝔐 is an ultraweakly continuous surjective *-linear mapping and d:𝔐→𝔐 is an ultraweakly continuous *-σ-derivation such that d(I) is a central element of 𝔐. We provide a Kadison–Sakai-type theorem by proving that ℌ can be decomposed into and d can be factored as the form , where δ:𝔐→𝔐 is an inner *-σ𝔎-derivation, Z is a central element, 2τ=2σ𝔏 is a *-homomorphism, and σ𝔎 and σ𝔏 stand for compressions of σ to 𝔎 and 𝔏 , respectively.

Keywords

derivation*-homomorphism*-σ-derivationinner σ-derivation*-(σ,τ)-derivationKadison–Sakai theoremultraweak (operator) topology

MSC classification

Secondary: 46L57: Derivations, dissipations and positive semigroups in $C^*$-algebras 47B47: Commutators, derivations, elementary operators, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 249 - 257
Copyright
Copyright © Australian Mathematical Society 2009

References

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