Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


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
MathSciNet review: 0318781
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a locally compact group G with property $ ({{\text{P}}_1})$, if there is a continuous projection of $ {L^1}(G)$ 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 $ {w^ \ast }$-closed left ideals.

Let G be further abelian and let I be a closed ideal in $ {L^1}(G)$. 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A20

Retrieve articles in all journals with MSC: 43A20

Additional Information

PII: S 0002-9947(1973)0318781-2
Keywords: Continuous projections, bounded approximate identities, closed left ideals, closed right ideals, closed 2-sided ideals, group algebras, modular functions, property $ {{\text{P}}_1}$, $ {w^ \ast }$-closed, Calderón set, spectral set, discrete coset ring, factorable closed ideals, Bohr compactification
Article copyright: © Copyright 1973 American Mathematical Society