CUBO A Mathematical Journal Vol.14, N° 01, (111-117). March 2012

More on Approximate Operators

Philip J. Maher and Mohammad Sal Moslehian

Mathematics And Statistics Group, Middlesex University, Hendon Campus, The Burrough, London Nw4 4 Bt, United Kingdom. email: p.maher@mdx.ac.uk

Department Of Pure Mathematics, Centre Of Excellence In Analysis On Algebraic Structures, (CEAAS), Ferdowsi University Of Mashhad, P.O. Box 1159, Mashhad 91775, Iran. email: moslehian@ferdowsi.um.ac.ir, moslehian@member.ams.org

ABSTRACT

This note is a continuation of the work on (p; )-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 .

Keywords and Phrases: Hilbert space; approximation; unitary; partial isometry; polar decomposition; (p; )-approximate operator

RESUMEN

Esta trabajo es una continuación del trabajo sobre operadores (p; )-aproximados estudiados por Mirzavaziri, Miura y Moslehian [4]. Investigamos isometrás parciales aproximadas e inversas aproximadas generalizadas. También probamos que si T es una contracción invertible que satisface entonces existe una isometría parcial V tal que

2010 AMS Mathematics Subject Classification: Primary 47A55; secondary 39B52.

References

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Received: June 2011. Revised: August 2011.