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A Generalized Fredholm Theory for Certain Maps in the Regular Representations of an Algebra

Published online by Cambridge University Press:  20 November 2018

Bruce Alan Barnes
Bruce Alan Barnes*
Affiliation:
The University of California, Berkeley, and The University of Oregon, Eugene
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Given an algebra A, the elements of A induce linear operators on A by left and right multiplication. Various authors have studied Banach algebras A with the property that some or all of these multiplication maps are completely continuous operators on A ; see (1-5). In (3)1. Kaplansky defined an element u of a Banach algebra A to be completely continuous if the maps a ⟶ ua and a ⟶ au, a ∊ A, are completely continuous linear operators.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 495 - 504
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This research was partially supported by National Science Foundation grant number GP-5585.

References

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