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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Multipliers with closed range on regular commutative Banach algebras
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by Pietro Aiena and Kjeld B. Laursen PDF
Proc. Amer. Math. Soc. 121 (1994), 1039-1048 Request permission

Abstract:

Conditions equivalent with closure of the range of a multiplier T, defined on a commutative semisimple Banach algebra A, are studied. A main result is that if A is regular then ${T^2}A$ is closed if and only if T is a product of an idempotent and an invertible. This has as a consequence that if A is also Tauberian then a multiplier with closed range is injective if and only if it is surjective. Several aspects of Fredholm theory and Kato theory are covered. Applications to group algebras are included.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 1039-1048
  • MSC: Primary 46J05; Secondary 43A22, 47B48
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1185257-1
  • MathSciNet review: 1185257