Universal objects in categories of reproducing kernels

DOI10.4171/RMI/632zbMath1234.46026arXiv0912.0091MaRDI QIDQ533384

Daniel Beltiţă, José E. Galé

Publication date: 3 May 2011

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0091

zbMATH Keywords

categoryvector bundlecompletely positive mappositive definite kernelGrassmannian manifoldReproducing kerneltautological bundleuniversal object

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Definitions and generalizations in theory of categories (18A05) Questions of holomorphy and infinite-dimensional manifolds (58B12) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (5)

Geometric Perspectives on Reproducing Kernels ⋮ Reproducing Kernels and Positivity of Vector Bundles in Infinite Dimensions ⋮ Linear connections for reproducing kernels on vector bundles ⋮ Some aspects of positive kernel method of quantization ⋮ Coherent state map quantization in a Hermitian-like setting

Cites Work

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• On complex infinite-dimensional Grassmann manifolds
• Geometric representation theory for unitary groups of operator algebras
• Holomorphic geometric models for representations of \(C^*\)-algebras
• On a construction of L. Hua for positive reproducing kernels
• On reproducing kernels and quantization of states
• Coherent states and geometric quantization
• Injectivity and operator spaces
• The relationship between a commutative Banach algebra and its maximal ideal space
• Completely positive maps of the Cuntz algebras
• Holomorphy and convexity in Lie theory
• On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions
• Irreducibility of certain unitary representations
• VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES AND UNIVERSALITY
• A tale of three kernels
• Maps on Complex Manifolds into Grassmann Spaces Defined by Reproducing Kernels of Bergman Type
• Theory of Reproducing Kernels
• The Stiefel bundle of a Banach algebra

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