Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Generalized open mapping theorems for bilinear maps, with an application to operator algebras

Author: P. G. Dixon
Journal: Proc. Amer. Math. Soc. 104 (1988), 106-110
MSC: Primary 46A30; Secondary 47A65, 47D25
MathSciNet review: 958052
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Cohen [4] gave an example of a surjective bilinear mapping between Banach spaces which was not open, and Horowitz [8] gave a much simpler example. We build on Horowitz' example to produce a similar result for bilinear mappings such that every element of the target space is a linear combination of $ n$ elements of the range. An immediate application is that Bercovici's construction [1] of an operator algebra with property $ ({\mathbb{A}_1})$ but not $ ({\mathbb{A}_1}(r))$ can be extended to achieve property $ ({\mathbb{A}_{1/n}})$ without $ ({\mathbb{A}_{1/n}}(r))$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A30, 47A65, 47D25

Retrieve articles in all journals with MSC: 46A30, 47A65, 47D25

Additional Information

PII: S 0002-9939(1988)0958052-0
Keywords: Open mapping theorem, bilinear map, dual algebra
Article copyright: © Copyright 1988 American Mathematical Society