Maximal abelian subalgebras of Banach algebras

Dales, H.G. and Pham, H.L. and Żelazko, W. (2021) Maximal abelian subalgebras of Banach algebras. Bulletin of the London Mathematical Society, 53 (6). pp. 1879-1897. ISSN 0024-6093

Full text not available from this repository.

Abstract

Let (Formula presented.) be a commutative, unital Banach algebra. We consider the number of different non-commutative, unital Banach algebras (Formula presented.) such that (Formula presented.) is a maximal abelian subalgebra in (Formula presented.). For example, we shall prove that, in the case where (Formula presented.) is an infinite-dimensional, unital Banach function algebra, (Formula presented.) is a maximal abelian subalgebra in infinitely-many closed subalgebras of (Formula presented.) such that no two distinct subalgebras are isomorphic; the same result holds for certain examples (Formula presented.) that are local algebras. We shall also give examples of uniform algebras of the form (Formula presented.), where (Formula presented.) is a compact space, with the property that there exists a family of arbitrarily large cardinality of pairwise non-isomorphic unital Banach algebras (Formula presented.) such that each (Formula presented.) contains (Formula presented.) as a closed subalgebra and is such that (Formula presented.) is a maximal abelian subalgebra in (Formula presented.).

Item Type:
Journal Article
Journal or Publication Title:
Bulletin of the London Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
162400
Deposited By:
Deposited On:
18 Nov 2021 13:30
Refereed?:
Yes
Published?:
Published
Last Modified:
22 Nov 2022 10:51