Vol. 2, No. 4, 2009

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Some numerical radius inequalities for Hilbert space operators

Mohsen Erfanian Omidvar, Mohammad Sal Moslehian and Assadollah Niknam

Vol. 2 (2009), No. 4, 471–478
Abstract

We present several numerical radius inequalities for Hilbert space operators. More precisely, we prove that if A,B,C,D B(H) and T = ABC D then max(w(A),w(D)) (12)(T + T212) and max((w(BC))12,(w(CB))12) (12)(T + T212). We also show that if A B(H) is positive, then

w(AX XA) 1 2A(X + X212).

Keywords
bounded linear operator, Hilbert space, norm inequality, numerical radius, positive operator
Mathematical Subject Classification 2000
Primary: 47A62
Secondary: 46C15, 47A30, 15A24
Milestones
Received: 5 May 2009
Accepted: 1 July 2009
Published: 28 October 2009

Communicated by Kenneth S. Berenhaut
Authors
Mohsen Erfanian Omidvar
Department of Mathematics
Faculty of Science
Islamic Azad University-Mashhad Branch
Mashhad 91722
Iran
Mohammad Sal Moslehian
Department of Pure Mathematics
Center of Excellence in Analysis on Algebraic Structures (CEAAS)
Ferdowsi University of Mashhad
P.O. Box 1159
Mashhad 91775
Iran
http://www.um.ac.ir/~moslehian
Assadollah Niknam
Department of Pure Mathematics
Center of Excellence in Analysis on Algebraic Structures (CEAAS)
Ferdowsi University of Mashhad
P.O. Box 1159
Mashhad 91775
Iran