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November 2020 A Fundamental Property of Bilinear Operators
Larry Downey
Missouri J. Math. Sci. 32(2): 128-137 (November 2020). DOI: 10.35834/2020/3202128

Abstract

In this paper, we address a fundamental question about the nature of bilinear operators first posed by Walter Rudin. While it has been known that there is not an open mapping theorem for bilinear operators in general, we show that bilinear operators enjoy an open mapping theorem, when the range has dimension three or less, and we address the simple, but crucial property that differentiates bilinear operators from their linear counterparts. We also give an example which shows that polynomials, in general do not enjoy an open mapping theorem, even when the range has dimension three.

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Larry Downey. "A Fundamental Property of Bilinear Operators." Missouri J. Math. Sci. 32 (2) 128 - 137, November 2020. https://doi.org/10.35834/2020/3202128

Information

Published: November 2020
First available in Project Euclid: 6 November 2020

MathSciNet: MR4171134
Digital Object Identifier: 10.35834/2020/3202128

Subjects:
Primary: 46G25
Secondary: 47H60‎

Rights: Copyright © 2020 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.32 • No. 2 • November 2020
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