Holomorphic spectral theory: a geometric approach

DOI10.1007/s11785-022-01238-3zbMath1503.47007OpenAlexW4281928020WikidataQ114221781 ScholiaQ114221781MaRDI QIDQ2148572

Mircea Martin

Publication date: 24 June 2022

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-022-01238-3

zbMATH Keywords

spectral theoryGrassmann manifoldscurvature invariantsHermitian holomorphic vector bundlesCowen-Douglas operators

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Subnormal operators, hyponormal operators, etc. (47B20) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Cowen-Douglas operators (47B13)

Cites Work

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• Rigidity of the flag structure for a class of Cowen-Douglas operators
• On the double commutant of Cowen-Douglas operators
• Hermitian geometry and involutive algebras
• On curvature and similarity
• On complex infinite-dimensional Grassmann manifolds
• Holomorphic geometric models for representations of \(C^*\)-algebras
• Equivalence of connections
• A unitary invariant for hyponormal operators
• Lectures on hyponormal operators
• Operators in Cowen-Douglas classes
• Curvature inequalities for operators of the Cowen-Douglas class
• A field-theoretic operator model and Cowen-Douglas class
• Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains
• Similarity of operators and geometry of eigenvector bundles
• Similarity classification of holomorphic curves
• Classification of quasi-homogeneous holomorphic curves and operators in the Cowen-Douglas class
• K-group and similarity classification of operators
• Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class
• Analytic projections, Corona problem and geometry of holomorphic vector bundles
• Curvature and the Backward Shift Operators
• Curvatures and Similarity of Operators with Holomorphic Eigenvectors
• The curvature invariant for a class of homogeneous operators
• Generalized Bergman Kernels and the Cowen-Douglas Theory
• On Weighted Shifts, Curvature and Similarity
• Similarity Classification of Cowen-Douglas Operators
• Operators in the Cowen-Douglas class and related topics
• A classification of homogeneous operators in the Cowen-Douglas class
• Complex geometry and operator theory
• A classification of homogeneous operators in the Cowen-Douglas class

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