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Titolo:
AN OPERATOR-INEQUALITY AND MATRIX NORMALITY
Autore:
JOHNSON CR; ZHANG FZ;
Indirizzi:
COLL WILLIAM & MARY,DEPT MATH WILLIAMSBURG VA 23185 UNIV CALIF SANTA BARBARA,DEPT MATH SANTA BARBARA CA 93106
Titolo Testata:
Linear algebra and its applications
, volume: 240, anno: 1996,
pagine: 105 - 110
SICI:
0024-3795(1996)240:<105:AOAMN>2.0.ZU;2-C
Fonte:
ISI
Lingua:
ENG
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
5
Recensione:
Indirizzi per estratti:
Citazione:
C.R. Johnson e F.Z. Zhang, "AN OPERATOR-INEQUALITY AND MATRIX NORMALITY", Linear algebra and its applications, 240, 1996, pp. 105-110

Abstract

Let A be a bounded linear operator on a Hilbert space H; denote \A\ =(AA)(1/2) and the norm of x is an element of H by \\x\\. It is proved that \(Au, v)\ less than or equal to \\\A\(alpha)u\\ \\\A\(1-alpha)v\\ For All u, v is an element of H for any 0 < alpha < 1. In particular, \(Au, v)\ less than or equal to (\A\u, u)(1/2)(\A\v, v)(1/2) ForAll u, v is an element of H. When H is of finite dimension, it is shown that A must be a normal operator if it satisfies \(Au, u)\ less than or equal to (\A\u, u)(alpha)(\A\u, u)(1-alpha) For All u is an element of H, for some real number alpha not equal 1/2.

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Documento generato il 26/09/20 alle ore 05:25:14