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- W1998351007 abstract "Abstract Let VN( G ) be the von Neumann algebra of a locally compact group G . We denote by μ the initial ordinal with |μ| equal to the smallest cardinality of an open basis at the unit of G and X = ﹛α ; α < μ﹜.We show that if G is nondiscrete then there exist an isometric *-isomorphism of l ∞ ( X ) into VN( G ) and a positive linear mapping π of VN( G ) onto l ∞ ( X ) such that π o = id l ∞ ( X ) and and π have certain additional properties. Let UCB((Ĝ)) be the C *–algebra generated by operators in VN( G ) with compact support and F (Ĝ) the space of all T ∈ VN( G ) such that all topologically invariant means on VN( G ) attain the same value at T . The construction of the mapping π leads to the conclusion that the quotient space UCB((Ĝ))/F((Ĝ)) ∪UCB((Ĝ)) has l ∞ ( X ) as a continuous linear image if G is nondiscrete. When G is further assumed to be non-metrizable, it is shown that UCB((Ĝ))/F((Ĝ)) ∪UCB((Ĝ)) contains a linear isomorphic copy of l ∞ ( X ). Similar results are also obtained for other quotient spaces." @default.
- W1998351007 created "2016-06-24" @default.
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- W1998351007 date "1997-12-01" @default.
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- W1998351007 title "The Von Neumann Algebra VN(G) of a Locally Compact Group and Quotients of Its Subspaces" @default.
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