Generalized open mapping theorems for bilinear maps, with an application to operator algebras
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- by P. G. Dixon PDF
- Proc. Amer. Math. Soc. 104 (1988), 106-110 Request permission
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
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 106-110
- MSC: Primary 46A30; Secondary 47A65, 47D25
- DOI: https://doi.org/10.1090/S0002-9939-1988-0958052-0
- MathSciNet review: 958052