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On the Spectrum of L ∞ (G)
Author(s) -
Lau A. T.,
Medghalchi A. R.,
Pym J. S.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-48.1.152
Subject(s) - locally compact space , compactification (mathematics) , mathematics , locally compact group , spectrum (functional analysis) , compact group , compact space , pure mathematics , product (mathematics) , algebraic number , discrete mathematics , algebra over a field , physics , lie group , mathematical analysis , quantum mechanics , geometry
We investigate the algebraic structure of the spectrum Ω of L ∞ (G) for a locally compact group G . In contrast to the compact and discrete cases, when G has neither of these properties, Ω is never a semigroup. For σcompact G we determine exactly when the product of two elements of Ω. is in Ω, but we present an example which suggests that for general groups the underlying set theory may have an effect. Our principal tool, which has independent interest, is a topological structure theorem for the L B ‐compactification of an arbitrary locally compact group.