More on approximate operators

Philip J. Maher; Mohammad Sal Moslehian

doi:10.4067/S0719-06462012000100009

Authors

Philip J. Maher Mathematics And Statistics Group, Middlesex University, Hendon Campus, The Burrough, London Nw4 4 Bt, United Kingdom.
Mohammad Sal Moslehian Department Of Pure Mathematics, Centre Of Excellence In Analysis On Algebraic Structures, (CEAAS), Ferdowsi University Of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.

DOI:

https://doi.org/10.4067/S0719-06462012000100009

Keywords:

Hilbert space, approximation, unitary, partial isometry, polar decomposition, (p, Îµ)-approximate operator

Abstract

This note is a continuation of the work on (p,Ñ”)–approximate operators studied by Mirzavaziri, Miura and Moslehian. [4]. We investigate approximate partial isometries and approximate generalized inverses. We also prove that if T is an invertible contraction satisfying . Then there exists a partial isometry V such that ”–T âˆ’ V”– < KÑ” for K > 0.