Operator inequalities related to the Corach–Porta–Recht inequality
Copyright policy )Operator inequalities related to the Corach–Porta–Recht inequality
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 $\left\Vert SXS^{-1}+S^{-1}XS+kX\right\Vert \geq (k+2)\left\Vert X\right\Vert$ under certain conditions.
12 Pages, to appear in Linear Algebra Appl. (LAA)
- National Scientific and Technical Research Council Argentina
- University of Tabuk Saudi Arabia
- National University of General Sarmiento Argentina
- Instituto de Ciencias Argentina
- Ferdowsi University of Mashhad Iran (Islamic Republic of)
Operator inequality, Numerical Analysis, Algebra and Number Theory, INVERTIBLE OPERATOR, 47B47 (Primary) 47A63, 47A30 (Secondary), Corach-Porta-Recht inequality, unitarily invariant norm, CORACH-PORTA-RECHT INEQUALITY, Unitarily invariant norm, Norms (inequalities, more than one norm, etc.) of linear operators, Invertible operator, Heinz inequality, Functional Analysis (math.FA), Mathematics - Functional Analysis, UNITARILY INVARIANT NORM, FOS: Mathematics, https://purl.org/becyt/ford/1.1, Discrete Mathematics and Combinatorics, Corach–Porta–Recht inequality, Linear operator inequalities, Geometry and Topology, https://purl.org/becyt/ford/1, HEINZ INEQUALITY, OPERATOR INEQUALITY
Operator inequality, Numerical Analysis, Algebra and Number Theory, INVERTIBLE OPERATOR, 47B47 (Primary) 47A63, 47A30 (Secondary), Corach-Porta-Recht inequality, unitarily invariant norm, CORACH-PORTA-RECHT INEQUALITY, Unitarily invariant norm, Norms (inequalities, more than one norm, etc.) of linear operators, Invertible operator, Heinz inequality, Functional Analysis (math.FA), Mathematics - Functional Analysis, UNITARILY INVARIANT NORM, FOS: Mathematics, https://purl.org/becyt/ford/1.1, Discrete Mathematics and Combinatorics, Corach–Porta–Recht inequality, Linear operator inequalities, Geometry and Topology, https://purl.org/becyt/ford/1, HEINZ INEQUALITY, OPERATOR INEQUALITY
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