Adjoint for operators in Banach spaces

Authors:
Tepper L. Gill, Sudeshna Basu, Woodford W. Zachary and V. Steadman

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1429-1434

MSC (2000):
Primary 46B99; Secondary 47D03

Published electronically:
September 22, 2003

MathSciNet review:
2053349

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well-known theorems of von Neumann and Lax. We also partially solve an open problem on the existence of a Markushevich basis with unit norm and prove that all closed densely defined linear operators on a separable Banach space can be approximated by bounded operators. This last result extends a theorem of Kaufman for Hilbert spaces and allows us to define a new metric for closed densely defined linear operators on Banach spaces. As an application, we obtain a generalization of the Yosida approximator for semigroups of operators.

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Additional Information

**Tepper L. Gill**

Affiliation:
Department of Electrical Engineering, Howard University, Washington, DC 20059

Email:
tgill@howard.edu

**Sudeshna Basu**

Affiliation:
Department of Mathematics, Howard University, Washington, DC 20059

Email:
sbasu@howard.edu

**Woodford W. Zachary**

Affiliation:
Department of Electrical Engineering, Howard University, Washington, DC 20059

Email:
wwzachary@earthlink.net

**V. Steadman**

Affiliation:
Department of Mathematics, University of the District of Columbia, Washington, DC 20058

DOI:
http://dx.doi.org/10.1090/S0002-9939-03-07204-6

Keywords:
Adjoints,
Banach space embeddings,
Hilbert spaces

Received by editor(s):
May 7, 2002

Received by editor(s) in revised form:
January 8, 2003

Published electronically:
September 22, 2003

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2003
American Mathematical Society