Unitarily invariant norm inequalities for operators

M. Erfanian Omidvar; M.S. Moslehian; A. Niknam

doi:10.1016/j.joems.2011.12.004

Journal of the Egyptian Mathematical Society (Apr 2012)

Unitarily invariant norm inequalities for operators

M. Erfanian Omidvar,
M.S. Moslehian,
A. Niknam

Affiliations

M. Erfanian Omidvar: Department of Mathematics, Faculty of Science, Mashhad Branch, Islamic Azad University, Mashhad, Iran
M.S. 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
A. 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

DOI: https://doi.org/10.1016/j.joems.2011.12.004
Journal volume & issue: Vol. 20, no. 1
pp. 38 – 42

Abstract

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We present several norm inequalities for Hilbert space operators. In particular, we prove that if A1,A2,…,An∈B(H), then |||A1A2∗+A2A3∗+⋯+AnA1∗|||⩽∑i=1nAiAi∗for all unitarily invariant norms. We also show that if A1,A2,A3,A4 are projections in B(H), then ∑i=14(-1)i+1Ai⊕0⊕0⊕0⩽|||(A1+|A3A1|)⊕(A2+|A4A2|)⊕(A3+|A1A3|)⊕(A4+|A2A4|)||| for any unitarily invariant norm.

Published in Journal of the Egyptian Mathematical Society

ISSN: 1110-256X (Print); 2090-9128 (Online)
Publisher: SpringerOpen
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics
Website: https://joems.springeropen.com/

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