Vol. 61, No. 1, 1975

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Linear operators for which TT and T + T commute

Stephen LaVern Campbell

Vol. 61 (1975), No. 1, 53–57
Abstract

This paper is about the bounded linear operators T acting in a separable Hilbert space h such that TT and T + T commute. It will be shown that such operators are normal if they are either compact or quasinilpotent. It is conjectured that if TT and T + T commute, then T = A + Q where A = A, AQ = QA, and Q is quasinormal. This conjecture is shown to be equivalent to [TT TT]T[TT TT] being hermitian.

Mathematical Subject Classification 2000
Primary: 47B99
Milestones
Received: 28 May 1975
Revised: 28 July 1975
Published: 1 November 1975
Authors
Stephen LaVern Campbell