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Hyper-Stonean envelopes of compact spaces

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Hyper-Stonean envelopes of compact spaces. / Dales, Harold Garth; Plebanek, Grzegorz.

In: Studia Mathematica, Vol. 246, 2019, p. 31-46.

Research output: Contribution to journalJournal article

Harvard

Dales, HG & Plebanek, G 2019, 'Hyper-Stonean envelopes of compact spaces', Studia Mathematica, vol. 246, pp. 31-46. https://doi.org/10.4064/sm170815-14-2

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Author

Dales, Harold Garth ; Plebanek, Grzegorz. / Hyper-Stonean envelopes of compact spaces. In: Studia Mathematica. 2019 ; Vol. 246. pp. 31-46.

Bibtex

@article{27218e9426db4755aeb2b86c82ba2b60,
title = "Hyper-Stonean envelopes of compact spaces",
abstract = "Let K be a compact space, and denote by (K) over tilde its hyper-Stonean envelope. We discuss the class of spaces K with the property that (K) over tilde is homeomorphic to (I) over tilde, the hyper-Stonean envelope of the closed unit interval d. Certainly each uncountable, compact, metrizable space K belongs to this class. We describe several further classes of compact spaces K for which (K) over tilde = (I) over tilde. In fact, (K) over tilde = (I) over tilde if and only if the Banach spaces M(K) and M(I) of measures on K and If are isometrically isomorphic.",
keywords = "Arens products, Borel measure, Corson compact, Eberlein compact, Maharam type, Rosenthal compact, biduals of Banach algebras, hyper-Stonean envelope, measure separable spaces",
author = "Dales, {Harold Garth} and Grzegorz Plebanek",
year = "2019",
doi = "10.4064/sm170815-14-2",
language = "English",
volume = "246",
pages = "31--46",
journal = "Studia Mathematica",
issn = "0039-3223",
publisher = "Instytut Matematyczny",

}

RIS

TY - JOUR

T1 - Hyper-Stonean envelopes of compact spaces

AU - Dales, Harold Garth

AU - Plebanek, Grzegorz

PY - 2019

Y1 - 2019

N2 - Let K be a compact space, and denote by (K) over tilde its hyper-Stonean envelope. We discuss the class of spaces K with the property that (K) over tilde is homeomorphic to (I) over tilde, the hyper-Stonean envelope of the closed unit interval d. Certainly each uncountable, compact, metrizable space K belongs to this class. We describe several further classes of compact spaces K for which (K) over tilde = (I) over tilde. In fact, (K) over tilde = (I) over tilde if and only if the Banach spaces M(K) and M(I) of measures on K and If are isometrically isomorphic.

AB - Let K be a compact space, and denote by (K) over tilde its hyper-Stonean envelope. We discuss the class of spaces K with the property that (K) over tilde is homeomorphic to (I) over tilde, the hyper-Stonean envelope of the closed unit interval d. Certainly each uncountable, compact, metrizable space K belongs to this class. We describe several further classes of compact spaces K for which (K) over tilde = (I) over tilde. In fact, (K) over tilde = (I) over tilde if and only if the Banach spaces M(K) and M(I) of measures on K and If are isometrically isomorphic.

KW - Arens products

KW - Borel measure

KW - Corson compact

KW - Eberlein compact

KW - Maharam type

KW - Rosenthal compact

KW - biduals of Banach algebras

KW - hyper-Stonean envelope

KW - measure separable spaces

U2 - 10.4064/sm170815-14-2

DO - 10.4064/sm170815-14-2

M3 - Journal article

VL - 246

SP - 31

EP - 46

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

ER -