Hilbert modules and complex analytic fibre spaces
type: Item
instance of: scholarly article
title: Hilbert modules and complex analytic fibre spaces
zbMATH Open document ID: 1487.32119
DOI: 10.4171/RLM/949
author: Harald Upmeier
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2022-02-15T00:00:00Z
review text: Summary: We describe the ``eigenbundle'' (localization bundle) of Hilbert modules over bounded symmetric domains and show that the fibres are closely related to Kähler geometry of certain flag manifolds defined in terms of Jordan algebras. This gives an intriguing relationship between Hilbert space operators, coherent module sheaves and geometry of Jordan manifolds. The resulting complex-analytic fibre spaces are stratified of arbitrary depth \(r\).
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 46E22
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 17C36
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 7473894
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: Hilbert module
zbMATH Keywords: complex-analytic fibre space
zbMATH Keywords: flag manifold
zbMATH Keywords: Jordan triple
MaRDI profile type: Publication
cites work: Q3617114
cites work: Homogeneous multiplication operators on bounded symmetric domains.
cites work: Unitary invariants for Hilbert modules of finite rank
cites work: Complex geometry and operator theory
cites work: Q3652526
cites work: Reproducing kernel functions and asymptotic expansions on Jordan-Kepler manifolds
cites work: Lineare Faserräume und kohärente Modulgarben über komplexen Räumen
cites work: Function spaces and reproducing kernels on bounded symmetric domains
cites work: Q4321748
cites work: Q3892778
cites work: A classification of homogeneous operators in the Cowen-Douglas class
cites work: Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen
cites work: Some combinatorial properties of Jack symmetric functions
cites work: Q5186182
cites work: Jordan Algebras and Harmonic Analysis on Symmetric Spaces
cites work: Toeplitz Operators on Bounded Symmetric Domains
cites work: Toeplitz \(C^*\)-algebras on bounded symmetric domains
full work available at URL: https://doi.org/10.4171/rlm/949
OpenAlex ID: W4200275120
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description: scientific article; zbMATH DE number 7473894