Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-15T17:24:50.814Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Barnes, B. A., Modular annihilator algebras, Can. J. Math., 18 (1966), 566–578.Google Scholar
2. Freundlich, M. F., Completely continuous elements of a nor med ring, Duke Math. J., 16 (1949), 273–283.Google Scholar
3. Kaplansky, I., Dual rings, Ann. of Math. (2), 49 (1948), 689–901.Google Scholar
4. Kaplansky, I., Normed algebras, Duke Math. J., 16 (1949), 399–418.Google Scholar
5. Olubummo, A., Left completely continuous B*-algebras, J. London Math. Soc, 32 (1957), 270–276.Google Scholar
6. Rickart, C. E., Banach algebras (Princeton, 1960).Google Scholar
7. Ruston, A. F., Operators with a Fredholm theory, J. London Math. Soc, 29 (1954), 318–326.Google Scholar
8. Taylor, A. E., Introduction to functional analysis (New York, 1958).Google Scholar
9. Taylor, A. E., Theorems on ascent, descent, nullity and defect of linear operators, Math. Ann., 168 (1966), 18–49.Google Scholar
10. Yood, B., Ideals in topological rings, Can. J. Math., 16 (1964), 28–45.Google Scholar