Toral and spherical Aluthge transforms of 2-variable weighted shifts

DOI10.1016/j.crma.2016.10.005zbMath1448.47046arXiv1611.00115OpenAlexW2537586349MaRDI QIDQ344332

Jasang Yoon, Raúl E. Curto

Publication date: 22 November 2016

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.00115

zbMATH Keywords

continuityhyponormality2-variable weighted shiftspherical Aluthge transformtoral Aluthge transform

Mathematics Subject Classification ID

Subnormal operators, hyponormal operators, etc. (47B20) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37)

Related Items (13)

Polynomial embeddings of unilateral weighted shifts in 2-variable weighted shifts ⋮ Spectra of the spherical Aluthge transform, the linear pencil, and a commuting pair of operators ⋮ Spherical Aluthge transform, sphericalpandlog-hyponormality of commuting pairs of operators ⋮ The spectral picture and joint spectral radius of the generalized spherical Aluthge transform ⋮ Generalized spherical Aluthge transforms and binormality for commuting pairs of operators ⋮ Spherical mean transform of operator pairs ⋮ Inequalities involving the generalized spherical Aluthge transform of operators ⋮ Upper bounds for the Euclidean spectral radius of operators via joint norms ⋮ Aluthge transforms of 2-variable weighted shifts ⋮ Aluthge transforms and common invariant subspaces for a commuting \(n\)-tuple of operators ⋮ Quasinormality of powers of commuting pairs of bounded operators ⋮ Joint numerical radius of spherical Aluthge transforms of tuples of Hilbert space operators ⋮ Joint spectra of spherical Aluthge transforms of commuting \(n\)-tuples of Hilbert space operators

Uses Software

• Mathematica

Cites Work

• Rigidity theorems for spherical hyperexpansions
• Subnormality of Aluthge transforms of weighted shifts
• Recursively generated weighted shifts and the subnormal completion problem
• Aluthge transforms of operators
• Dilations and commutant lifting for jointly isometric operators -- a geometric approach
• Schur product techniques for the subnormality of commuting 2-variable weighted shifts
• Subnormality of 2-variable weighted shifts with diagonal core
• \(k\)-Hyponormality of multivariable weighted shifts
• On p-hyponormal operators for \(0<p<1\)
• On the reflexivity of certain operator tuples
• Jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal
• Brown measure and iterates of the Aluthge transform for some operators arising from measurable actions
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