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Ring Theory Session of the fourth joint meeting of the American Mathematical Society and the Sociedad Matematica Mexicana
May 19-22, 1999
University of North Texas
Denton, TX, USA

Organizers
Ricardo Alfaro, Carlos Signoret, Sergio R. Lopez-Permouth

View Abstracts

Quotient rings of algebras of functions and operators
by
S. K. Jain
Ohio University
Coauthors: Ajit I. Singh

Various quotient rings of rings B of Banach algebra A-valued continuous functions on a completely regular Hausdorff Space X are constructed in terms of continuous functions defined on dense open subsets of X taking values in the maximal quotient ring of the Banach algebra A. This extends the results proved by N. J. Fine, L. Gillman, and J. Lambek (1965) for the case of A, the field of real numbers. The pattern is similar and utilizes as well as generalizes the results proved for algebras of multipliers of B by C. A. Akemann, G. K. Pedersen and J. Tomiyama (1973). The techniques combine those from algebra, analysis and topology. The details of the cases when A is the normed division algebra of real quaternions or the operator algebra \QTRcalB(H) of a Hilbert space \QTRcalH are given to illustrate different situations of our results.

Date received: March 23, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabz-13.