On the operator equation

Author:
Jerome A. Goldstein

Journal:
Proc. Amer. Math. Soc. **70** (1978), 31-34

MSC:
Primary 47A60; Secondary 47B25

DOI:
https://doi.org/10.1090/S0002-9939-1978-0477836-2

MathSciNet review:
0477836

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the operator equation ; here *A* and *B* are (possibly unbounded) selfadjoint operators and *Q* is a bounded operator on a Hilbert space. The theory of one parameter semigroups of operators is applied to give a quick derivation of M. Rosenblum's formula for approximate solutions of . Sufficient conditions are given in order that has a solution in the Schatten-von Neumann class if *Q* is in . Finally a sufficient condition for solvability of is given in terms of T. Kato's notion of smoothness.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0477836-2

Keywords:
Hilbert space,
selfadjoint operator,
operator equation,
compact operator,
Schatten-von Neumann class,
one-parameter group of isometries

Article copyright:
© Copyright 1978
American Mathematical Society