Adjoint for Operators in Banach Spaces

Details Adjoint for Operators in Banach Spaces Adjoint for Operators in Banach Spaces

2004-05-25

arxiv.org/abs/math-ph/0405060v1

Proc. Amer. Math. Soc. 132 (2004), 1429

Physics

Mathematical Physics

Scientific paper

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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