## 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