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

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

 

An elementary counterexample to the open mapping principle for bilinear maps


Author: Charles Horowitz
Journal: Proc. Amer. Math. Soc. 53 (1975), 293-294
MSC: Primary 32A99
MathSciNet review: 0419813
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In [2], Rudin asked whether a continuous bilinear map from the product of two Banach spaces onto a Banach space must be open at the origin; i.e., whether under such a map the image of every neighborhood of zero must contain a neighborhood of zero. Recently, Cohen [1] showed that the answer to the general question was in the negative. However, his counterexample was somewhat involved and left the issue unresolved for bilinear maps on Hilbert spaces. The purpose of this note is to show that the open mapping principle for bilinear maps, as described above, fails even in the finite dimensional case.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32A99

Retrieve articles in all journals with MSC: 32A99


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0419813-0
PII: S 0002-9939(1975)0419813-0
Article copyright: © Copyright 1975 American Mathematical Society