Schatten class and Berezin transform of quaternionic linear operators

DOI10.1002/mma.3944zbMath1356.47025arXiv1511.07308OpenAlexW3123420816MaRDI QIDQ5507183

Tim Janssens, Jonathan Gantner, Fabrizio Colombo

Publication date: 16 December 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07308

zbMATH Keywords

Schatten class of operatorsBerezin transform of quaternionic operatorsspectral theorem and the \(S\)-spectrumweighted Bergman spaces of slice hyperholomorphic functions

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Functional calculus for linear operators (47A60) Spectrum, resolvent (47A10)

Related Items (9)

Slice regular weighted composition operators ⋮ On the weak topology of quaternionic Hilbert spaces ⋮ On power series expansions of the \(S\)-resolvent operator and the Taylor formula ⋮ Novel sampling formulas associated with quaternionic prolate spheroidal wave functions ⋮ Quaternionic triangular linear operators ⋮ Concept of s-numbers in quaternionic analysis and Schatten classes ⋮ The correct formulation of Gleason's theorem in quaternionic Hilbert spaces ⋮ Some inequalities for selfadjoint operators on quaternionic Hilbert spaces ⋮ Perturbation of normal quaternionic operators

Cites Work

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• The spectral theorem for unitary operators based on the \(S\)-spectrum
• Slice hyperholomorphic Schur analysis
• Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions
• Schur functions and their realizations in the slice hyperholomorphic setting
• Krein-Langer factorization and related topics in the slice hyperholomorphic setting
• A new resolvent equation for the \(S\)-functional calculus
• Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
• Quaternion quantum mechanics: Second quantization and gauge fields
• On the formulations of the quaternionic functional calculus
• The spectral theorem in quaternions
• Bloch, Besov and Dirichlet spaces of slice hyperholomorphic functions
• On some properties of the quaternionic functional calculus
• Realizations of slice hyperholomorphic generalized contractive and positive functions
• The logic of quantum mechanics
• The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum
• Formulations of the -functional calculus and some consequences
• CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES
• The C-property for slice regular functions and applications to the Bergman space
• Regular Functions of a Quaternionic Variable
• The Fock Space in the Slice Hyperholomorphic Setting
• Functions of the infinitesimal generator of a strongly continuous quaternionic group
• Spectral theory for unitary operators on a quaternionic Hilbert space
• The Fueter mapping theorem in integral form and the ℱ-functional calculus
• On slice biregular functions and isomorphisms of Bergman spaces
• A class of vector coherent states defined over matrix domains
• On Two Approaches to the Bergman Theory for Slice Regular Functions
• Normal Operators on Quaternionic Hilbert Spaces

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