# Norm Inequalities in Operator Ideals

@article{Larotonda2008NormII, title={Norm Inequalities in Operator Ideals}, author={G. Larotonda}, journal={Journal of Functional Analysis}, year={2008}, volume={255}, pages={3208-3228} }

Abstract In this paper we introduce a new technique for proving norm inequalities in operator ideals with a unitarily invariant norm. Among the well-known inequalities which can be proved with this technique are the Lowner–Heinz inequality, inequalities relating various operator means and the Corach–Porta–Recht inequality. We prove two general inequalities and from them we derive several inequalities by specialization, many of them new. We also show how some inequalities, known to be valid for… Expand

#### 14 Citations

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Abstract Let ( I , ⦀ . ⦀ ) be a norm ideal of operators equipped with a unitarily invariant norm ⦀ . ⦀ . We exploit integral representations of certain functions to prove that certain ratios of… Expand

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Abstract The aim of this work is to apply the complex interpolation method to norms of n -tuples of operators in a symmetrically-normed ideal J ϕ ⊆ B ( H ) defined by a ϕ symmetric norming function… Expand

A note on the paper “Norm inequalities in operator ideals” [J. Funct. Anal. 255 (11) (2008), 3208–3228] by G. Larotonda

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Abstract In this note we show that the presented proof of [1, th. 12] , being based on a false statement appearing in this proof, is not viable for all of the proclaimed values of the involved… Expand

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In this article we study the Heinz and Hermite-Hadamard inequalities. We derive the whole series of refinements of these inequalities involving unitarily invariant norms, which improve some recent… Expand

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In this paper, we present new properties of the space L 1 ( M, τ ) of integrable (with respect to the trace τ ) operators affiliated to a semifinite von Neumann algebra M . For self-adjoint τ… Expand

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where s1(A) ≥ s2(A) ≥ ... ≥ sn(A) are the singular values of A, which are the eigenvalues of the positive semidefinite matrix | A |= (AA) 1 2 , arranged in decreasing order and repeated according to… Expand

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Abstract We study the geometry of the set Δ p , with 1 p ∞ , which consists of perturbations of the identity operator by p-Schatten class operators, which are positive and invertible as elements of B… Expand

Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces

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Abstract We study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study… Expand

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