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On the invertibility of the mapT→STS−1+S−1TSand operator-norm inequalities

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
183
Identifiers
DOI: 10.1016/0024-3795(93)90427-p

Abstract

Abstract For an invertible operator S, we consider the invertibility of the map T→ STS −1 + S −1 TS. When this map is not invertible, the kernel is examined. For a normal invertible operator N, a condition on the spectrum of N is found to be equivalent to the invertibility of the map T→ NTN −1+ N −1 TN.

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