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