A note on norm ideals and the operatorX→AX−XB |
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Authors: | Lawrence A Fialkow |
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Institution: | (1) Department of Mathematics, Western Michigan University, 49008 Kalamazoo, Michigan, USA |
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Abstract: | For operatorsA andB on a Hilbert space ℋ, let τ denote the operator on ℒ(ℋ) defined by τ(X)=AX−XB. Several equivalent conditions are given for τ to be surjective or bounded below. Analogues of these results are given for
the restrictions of τ to norm ideals, and the norms of these restrictions are estimated.
The author gratefully acknowledges support by a grant from the National Science Foundation. |
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