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Operator inequalities related to the Corach–Porta–Rechtinequality

Citation:

C C, M.S M, A S. Operator inequalities related to the Corach–Porta–Rechtinequality. Linear Algebra Appl. 2012;436 :3008-3017.
operator_inequalities_related_to_cpr_ineq.pdf268 KB

Abstract:

We prove some refinements of an inequality due to X. Zhan in an
arbitrary complex Hilbert space by using some results on the Heinz
inequality. We present several related inequalities as well as new
variants of the Corach–Porta–Recht inequality.We also characterize
the class of operators satisfying
SXS
−1 + S
−1XS + kX

(k +
2) X under certain conditions.