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Maximal abelian subalgebras of Banach algebras

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Maximal abelian subalgebras of Banach algebras. / Dales, H.G.; Pham, H.L.; Żelazko, W.
In: Bulletin of the London Mathematical Society, Vol. 53, No. 6, 31.12.2021, p. 1879-1897.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Dales, HG, Pham, HL & Żelazko, W 2021, 'Maximal abelian subalgebras of Banach algebras', Bulletin of the London Mathematical Society, vol. 53, no. 6, pp. 1879-1897. https://doi.org/10.1112/blms.12551

APA

Dales, H. G., Pham, H. L., & Żelazko, W. (2021). Maximal abelian subalgebras of Banach algebras. Bulletin of the London Mathematical Society, 53(6), 1879-1897. https://doi.org/10.1112/blms.12551

Vancouver

Dales HG, Pham HL, Żelazko W. Maximal abelian subalgebras of Banach algebras. Bulletin of the London Mathematical Society. 2021 Dec 31;53(6):1879-1897. Epub 2021 Nov 4. doi: 10.1112/blms.12551

Author

Dales, H.G. ; Pham, H.L. ; Żelazko, W. / Maximal abelian subalgebras of Banach algebras. In: Bulletin of the London Mathematical Society. 2021 ; Vol. 53, No. 6. pp. 1879-1897.

Bibtex

@article{069ea421cdf5427facc414f676b7e4ec,
title = "Maximal abelian subalgebras of Banach algebras",
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.). ",
keywords = "46H10 (primary)",
author = "H.G. Dales and H.L. Pham and W. {\.Z}elazko",
year = "2021",
month = dec,
day = "31",
doi = "10.1112/blms.12551",
language = "English",
volume = "53",
pages = "1879--1897",
journal = "Bulletin of the London Mathematical Society",
issn = "0024-6093",
publisher = "Oxford University Press",
number = "6",

}

RIS

TY - JOUR

T1 - Maximal abelian subalgebras of Banach algebras

AU - Dales, H.G.

AU - Pham, H.L.

AU - Żelazko, W.

PY - 2021/12/31

Y1 - 2021/12/31

N2 - 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.).

AB - 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.).

KW - 46H10 (primary)

U2 - 10.1112/blms.12551

DO - 10.1112/blms.12551

M3 - Journal article

VL - 53

SP - 1879

EP - 1897

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 6

ER -