Some characterizations of the automorphisms of $B(H)$ and $C(X)$

DOI10.1090/S0002-9939-01-06172-XzbMath0983.47024arXivmath/0011030OpenAlexW1637991375MaRDI QIDQ2750894

Publication date: 21 October 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0011030

zbMATH Keywords

automorphism operator algebra function algebra spectrum preserving properties

Mathematics Subject Classification ID

Banach algebras of continuous functions, function algebras (46J10) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

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Cites Work