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ELA

BOUNDS ON THE SPECTRAL RADIUS OF

HADAMARD PRODUCTS OF POSITIVE

OPERATORS ON

ℓ

P

-SPACES

∗

ANTON R. SCHEP†

Abstract. Recently, K.M.R. Audenaert (2010), and R.A. Horn and F. Zhang (2010) proved inequalities between the spectral radius of Hadamard products of finite nonnegative matrices and the spectral radius of their ordinary matrix product. We will prove these inequalities in such a way that they extend to infinite nonnegative matricesAand Bthat define bounded operators on the

classical sequence spacesℓp.

Key words.Hadamard product, Spectral radius, Nonnegative matrix, Positive operator, Matrix Inequality.

AMS subject classifications. 15A45, 15B48, 47B65.

∗Received by the editors on November 15, 2010. Accepted for publication on April 16, 2011.

Handling Editor: Roger A. Horn.

†Department of Mathematics, University of South Carolina, Columbia, SC 29212, USA

([email protected]).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 22, pp. 443-447, April 2011

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