Abstract
Let B be an abstract Segal algebra in some Banach algebra A. There was some belief that in the commutative case A should be semi-simple, if B is, but this is not so (Section I). It is well known that a (proper) abstract Segal algebra does not have bounded right approximate units. It may however have a left unit. Pseudosymmetric Segal algebras in the sense of Reiter do not have bounded left approximate units (Section II). A nonfactorization proof is given for a class of algebras which contains most of the known examples of Segal algebras on abelian groups (Section III).
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Leinert, M. Remarks on Segal algebras. Manuscripta Math 16, 1–9 (1975). https://doi.org/10.1007/BF01169059
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DOI: https://doi.org/10.1007/BF01169059