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

 

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: 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
PII: S 0002-9939(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