Operators similar to unitary or selfadjoint ones

Johannes A. Van Casteren

Vol. 104 (1983), No. 1, 241–255

DOI: 10.2140/pjm.1983.104.241

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