Vol. 104, No. 1, 1983

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Operators similar to unitary or selfadjoint ones

Johannes A. Van Casteren

Vol. 104 (1983), No. 1, 241–255
Abstract

Let T be a bounded linear operator on a Hilbert space. General necessary and sufficient conditions are given in order that V TV 1 is unitary for some bounded linear operator V with bounded everywhere defined inverse. Similarly let B be a closed and densely defined linear operator in a Hilbert space. General necessary and sufficient conditions are given in order that V BV 1 is selfadjoint for some bounded linear operator V with bounded everywhere defined inverse.

Mathematical Subject Classification 2000
Primary: 47A65
Secondary: 47B25
Milestones
Received: 27 February 1981
Revised: 14 September 1981
Published: 1 January 1983
Authors
Johannes A. Van Casteren