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Quasianalytic Banach function algebras

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Quasianalytic Banach function algebras. / Dales, H.G.; Davie, A. M.
In: Journal of Functional Analysis, Vol. 13, No. 1, 05.1973, p. 28-50.

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

Harvard

Dales, HG & Davie, AM 1973, 'Quasianalytic Banach function algebras', Journal of Functional Analysis, vol. 13, no. 1, pp. 28-50. https://doi.org/10.1016/0022-1236(73)90065-7

APA

Dales, H. G., & Davie, A. M. (1973). Quasianalytic Banach function algebras. Journal of Functional Analysis, 13(1), 28-50. https://doi.org/10.1016/0022-1236(73)90065-7

Vancouver

Dales HG, Davie AM. Quasianalytic Banach function algebras. Journal of Functional Analysis. 1973 May;13(1):28-50. doi: 10.1016/0022-1236(73)90065-7

Author

Dales, H.G. ; Davie, A. M. / Quasianalytic Banach function algebras. In: Journal of Functional Analysis. 1973 ; Vol. 13, No. 1. pp. 28-50.

Bibtex

@article{79d4ece2e274489bbe999ce19da6646b,
title = "Quasianalytic Banach function algebras",
abstract = "We construct certain Banach algebras of infinitely differentiable functions on compact plane sets such that the algebras are quasianalytic, and we use these algebras to construct examples of Banach algebras defined on their maximal ideal spaces which, first, have only countably many peak points and, second, have the property that a discontinuous function operates on the algebra. We show that any function defined on an open subset of the plane which operates on a Banach function algebra is necessarily continuous on a dense open subset of its domain.",
author = "H.G. Dales and Davie, {A. M.}",
year = "1973",
month = may,
doi = "10.1016/0022-1236(73)90065-7",
language = "English",
volume = "13",
pages = "28--50",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Quasianalytic Banach function algebras

AU - Dales, H.G.

AU - Davie, A. M.

PY - 1973/5

Y1 - 1973/5

N2 - We construct certain Banach algebras of infinitely differentiable functions on compact plane sets such that the algebras are quasianalytic, and we use these algebras to construct examples of Banach algebras defined on their maximal ideal spaces which, first, have only countably many peak points and, second, have the property that a discontinuous function operates on the algebra. We show that any function defined on an open subset of the plane which operates on a Banach function algebra is necessarily continuous on a dense open subset of its domain.

AB - We construct certain Banach algebras of infinitely differentiable functions on compact plane sets such that the algebras are quasianalytic, and we use these algebras to construct examples of Banach algebras defined on their maximal ideal spaces which, first, have only countably many peak points and, second, have the property that a discontinuous function operates on the algebra. We show that any function defined on an open subset of the plane which operates on a Banach function algebra is necessarily continuous on a dense open subset of its domain.

U2 - 10.1016/0022-1236(73)90065-7

DO - 10.1016/0022-1236(73)90065-7

M3 - Journal article

VL - 13

SP - 28

EP - 50

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 1

ER -