Abstract

CANO, Cristina; MOSCONI, Irene  and  STOJANOFF, Demetrio. Some operator inequalities for unitarily invariant norms. Rev. Unión Mat. Argent. [online]. 2005, vol.46, n.1, pp.53-66. ISSN 0041-6932.

Let be the algebra of bounded operators on a complex separable Hilbert space . Let be a unitarily invariant norm defined on a norm ideal . Given two positive invertible operators and , we show that , . This extends Zhang’s inequality for matrices. We prove that this inequality is equivalent to two particular cases of itself, namely and . We also characterize those numbers such that the map given by is invertible, and we estimate the induced norm of acting on the norm ideal . We compute sharp constants for the involved inequalities in several particular cases.

Keywords : Positive matrices; Inequalities; Unitarily invariant norm.

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