abs_vol20_pp506-518. 21KB Jun 04 2011 12:05:48 AM

ELA

POLYNOMIAL INEQUALITIES FOR NON-COMMUTING

OPERATORS

∗

JOHN E. MCCARTHY† _{AND RICHARD M. TIMONEY}‡

Abstract. We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.

Key words. Ando inequality, Non-commuting, Symmetric functional calculus.

AMS subject classifications.15A60.

∗_{Received by the editors April 13, 2010. Accepted for publication August 8, 2010. Handling}

Editor: Harm Bart.

†_{Washington University, St. Louis and Trinity College, Dublin (mccarthy@wustl.edu). Partially}

supported by National Science Foundation Grants DMS 0501079 and DMS 0966845.

‡_{Trinity College, Dublin (richardt@maths.tcd.ie).}

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 20, pp. 506-518, August 2010