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Approximation by partial isometries

Published online by Cambridge University Press:  20 January 2009

Pei Yuan Wu
Pei Yuan Wu
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, Republic of China
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Let B(H) be the algebra of bounded linear operators on a complex separable Hilbert space H. The problem of operator approximation is to determine how closely each operator T ∈B(H) can be approximated in the norm by operators in a subset L of B(H). This problem is initiated by P. R. Halmo [3] when heconsidered approximating operators by the positive ones. Since then, this problem has been attacked with various classes L: the class of normal operators whose spectrum is included in a fixed nonempty closed subset of the complex plane [4], the classes of unitary operators [6] and invertible operators [1]. The purpose of this paper is to study the approximation by partial isometries.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 2 , June 1986 , pp. 255 - 261
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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