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## Second duals of measure algebras

Autorzy
Seria
Rozprawy Matematyczne tom/nr w serii: 481 wydano: 2011
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Warianty tytułu
Abstrakty
EN
Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L¹(G) and the measure algebra M(G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C₀(Ω)'' of the C*-algebra C₀(Ω) for a locally compact space Ω, recognizing this space as C(Ω̃), where Ω̃ is the hyper-Stonean envelope of Ω.
We shall study the C*-algebra $B^{b}(Ω)$ of bounded Borel functions on Ω, and we shall determine the exact cardinality of a variety of subsets of Ω̃ that are associated with $B^{b}(Ω)$.
We shall identify the second duals of the measure algebra (M(G),∗) and the group algebra (L¹(G),∗) as the Banach algebras (M(G̃),□ ) and (M(Φ),□ ), respectively, where □ denotes the first Arens product and G̃ and Φ are certain compact spaces, and we shall then describe many of the properties of these two algebras. In particular, we shall show that the hyper-Stonean envelope G̃ determines the locally compact group G. We shall also show that (G̃,□ ) is a semigroup if and only if G is discrete, and we shall discuss in considerable detail the product of point masses in M(G̃). Some important special cases will be considered.
We shall show that the spectrum of the C*-algebra $L^{∞}(G)$ is determining for the left topological centre of L¹(G)'', and we shall discuss the topological centre of the algebra (M(G)'',□ ).
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Miejsce publikacji
Warszawa
Seria
Rozprawy Matematyczne tom/nr w serii: 481
Liczba stron
121
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
• Department of Mathematics and Statistics, Fylde College, University of Lancaster, Lancaster LA1 4YF, United Kingdom
autor
• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
autor
• Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
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 EN
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