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HOW AND WHY TO SOLVE THE OPERATOR EQUATION AX−XB = Y

Published online by Cambridge University Press:  01 January 1997

RAJENDRA BHATIA  and
PETER ROSENTHAL
RAJENDRA BHATIA
Affiliation:
Indian Statistical Institute, New Delhi 110016, India
PETER ROSENTHAL
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
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Abstract

The entities A, B, X, Y in the title are operators, by which we mean either linear transformations on a finite-dimensional vector space (matrices) or bounded (= continuous) linear transformations on a Banach space. (All scalars will be complex numbers.) The definitions and statements below are valid in both the finite-dimensional and the infinite-dimensional cases, unless the contrary is stated.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 1 , January 1997 , pp. 1 - 21
Copyright
© The London Mathematical Society 1997

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