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Derivations from Hereditary Subalgebras of C*-Algebras

Published online by Cambridge University Press:  20 November 2018

A. J. Lazar ,
S.-K. Tsui  and
S. Wright
A. J. Lazar
Affiliation:
Tel-Aviv University, Tel-Aviv, Israel
S.-K. Tsui
Affiliation:
Oakland University, Rochester, Michigan
S. Wright
Affiliation:
Oakland University, Rochester, Michigan
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Let A be a C*-algebra, B a C*-subalgebra of A, δ:B → A a derivation, i.e., a linear map with

There has been considerable interest for several years now in the question of when δ can be extended from B to a derivation of A (see, for example, [8], Section 4, [1], [5], [4], [6], [9], [10], [11]). The paper before the reader will be concerned with this extension problem when B is a hereditary C*-subalgebra of A.

Our work takes its cue from the paper [6] of George Elliott. We prove in Section 2 of the present paper that derivations as described above of a unital hereditary C*-subalgebra always extend whenever A is either simple, AW*, separable and AF, or separable with continuous trace, thus generalizing and extending Theorem 4.5 of [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 1 , 01 February 1986 , pp. 109 - 126
Copyright
Copyright © Canadian Mathematical Society 1986

References

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