Vol. 70, No. 1, 1977

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ISSN: 0030-8730
A note on quasisimilarity. II

Lawrence Arthur Fialkow

Vol. 70 (1977), No. 1, 151–162
Abstract

Let denote a separable, infinite dimensional complex Hilbert space, and let () denote the algebra of all bounded linear operators on . An operator X in () is a quasiaffinity (or a quasi-invertible operator) if X is injective and has dense range. An operator A on is a quasiaffine transform of operator B if there exists a quasiaffinity such that BX = XA. A and B are quasisimilar if they are quasiaffine transforms of one another. The purpose of this note is to study the quasisimilarity orbits of certain subsets of () containing quasinilpotent, spectral, and compact operators.

Mathematical Subject Classification 2000
Primary: 47A65
Secondary: 47B40, 47B05
Milestones
Received: 16 July 1976
Revised: 2 March 1977
Published: 1 May 1977
Authors
Lawrence Arthur Fialkow