Representations of hermitian kernels by means of Kreĭn spaces

DOI10.2977/prims/1195144882zbMath0904.46016OpenAlexW2094689392MaRDI QIDQ1265293

Aurelian Gheondea, Tiberiu Constantinescu

Publication date: 21 January 1999

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195144882

zbMATH Keywords

Hermitian kernelskernels of positive typeinduced Kreĭn spaceKolmogorov decompositionsNaĭmark dilationsreproducing kernel Kreĭn spacesToeplitz Hermitian kernels

Mathematics Subject Classification ID

Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (15)

Reproducing Kernel Kreĭn Spaces ⋮ POSITIVE DEFINITE MAPS, REPRESENTATIONS AND FRAMES ⋮ Operators which preserve a positive definite inner product ⋮ Hermitian kernels with bounded structure ⋮ Embeddings, operator ranges, and Dirac operators ⋮ Reproducing kernel almost Pontryagin spaces ⋮ Closely embedded Kreĭn spaces and applications to Dirac operators ⋮ Dilations of some VH-spaces operator valued invariant kernels ⋮ Representations of \(\ast\)-semigroups associated to invariant kernels with values adjointable operators ⋮ Parrott's theorem and bounded solutions of a system of operator equations ⋮ Covariant representations on Krein \(C^\ast\)-modules associated to pairs of two maps ⋮ On L.\ Schwartz's boundedness condition for kernels ⋮ Krein reproducing kernel modules in Clifford analysis ⋮ Absolute continuity for operator valued completely positive maps on C∗-algebras ⋮ Joint functional calculus for definitizable self-adjoint operators on Krein spaces

Cites Work

• Selfpolar norms on an indefinite inner product space
• Operator inequalities and construction of Krein spaces
• The essential uniqueness property for operators on Kreĭn spaces
• Some remarks on reproducing kernel Krein spaces
• Positive definite kernels, continuous tensor products, and central limit theorems of probability theory
• Sous-espaces d'espaces vectoriels topologiques et noyaux associés. (Noyaux reproduisants.)
• Symmetrizable completely continuous linear transformations in Hilbert space
• Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im RaumeIIx zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen
• Theory of Reproducing Kernels
• Symmetrizable linear transformations
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