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

RAJENDRA BHATIA; PETER ROSENTHAL

doi:10.1112/S0024609396001828

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.

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

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