λ-Aluthge transforms and Schatten ideals

Let T∈L(H), and let T = U|T| = |T*|U be the polar decomposition of T. Then, for every λ ∈ [0, 1] the λ-Aluthge transform is defined by Δλ(T) = |T|λU|T| 1-λ. We show that several properties which are known for the usual Aluthge transform (i.e. the case λ = 1/2) also hold for λ-Aluthge transforms with...

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Bibliographic Details
Authors: Antezana, Jorge Abel, Massey, Pedro Gustavo, Stojanoff, Demetrio
Format: article
Status:Published version
Publication Date:2005
Country:Argentina
Institution:Universidad Nacional de La Plata
Repository:SEDICI (UNLP)
Language:English
OAI Identifier:oai:sedici.unlp.edu.ar:10915/83154
Online Access:http://sedici.unlp.edu.ar/handle/10915/83154
Access Level:Open access
Keyword:Matemática
Aluthge transform
Polar decomposition
Riesz calculus
Schatten norms
Description
Summary:Let T∈L(H), and let T = U|T| = |T*|U be the polar decomposition of T. Then, for every λ ∈ [0, 1] the λ-Aluthge transform is defined by Δλ(T) = |T|λU|T| 1-λ. We show that several properties which are known for the usual Aluthge transform (i.e. the case λ = 1/2) also hold for λ-Aluthge transforms with λ ∈ (0, 1). Moreover, we get several results which are new, even for the usual Aluthge transform.