Projections and approximate identities for ideals in group algebras
Authors:
Teng-Sun Liu, Arnoud van Rooij and Ju Kwei Wang
Journal:
Trans. Amer. Math. Soc. 175 (1973), 469-482
MSC:
Primary 43A20
DOI:
https://doi.org/10.1090/S0002-9947-1973-0318781-2
MathSciNet review:
0318781
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Abstract | References | Similar Articles | Additional Information
Abstract: For a locally compact group G with property , if there is a continuous projection of
onto a closed left ideal I, then there is a bounded right approximate identity in I. If I is further 2-sided, then I has a 2-sided approximate identity. The converse is proved for
-closed left ideals.
Let G be further abelian and let I be a closed ideal in . The condition that I has a bounded approximate identity is characterized in a number of ways which include (1) the factorability of I, (2) that the hull of I is in the discrete coset ring of the dual group, and (3) that I is the kernel of a closed element in the discrete coset ring of the dual group.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1973-0318781-2
Keywords:
Continuous projections,
bounded approximate identities,
closed left ideals,
closed right ideals,
closed 2-sided ideals,
group algebras,
modular functions,
property ,
-closed,
Calderón set,
spectral set,
discrete coset ring,
factorable closed ideals,
Bohr compactification
Article copyright:
© Copyright 1973
American Mathematical Society