A Bochner type theorem for inductive limits of Gelfand pairs

Marouane Rabaoui[1]

  • [1] Université Paul Verlaine-Metz Laboratoire de Mathématiques et Applications de Metz Bât. A Île de Saulcy 57045 Metz cedex 01 (France)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 5, page 1551-1573
  • ISSN: 0373-0956

Abstract

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In this article, we prove a generalisation of Bochner-Godement theorem. Our result deals with Olshanski spherical pairs ( G , K ) defined as inductive limits of increasing sequences of Gelfand pairs ( G ( n ) , K ( n ) ) n ≥ 1 . By using the integral representation theory of G. Choquet on convex cones, we establish a Bochner type representation of any element ϕ of the set 𝒫 ♮ ( G ) of K -biinvariant continuous functions of positive type on G .

How to cite

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Rabaoui, Marouane. "A Bochner type theorem for inductive limits of Gelfand pairs." Annales de l’institut Fourier 58.5 (2008): 1551-1573. <http://eudml.org/doc/10356>.

@article{Rabaoui2008,
abstract = {In this article, we prove a generalisation of Bochner-Godement theorem. Our result deals with Olshanski spherical pairs $(G, K)$ defined as inductive limits of increasing sequences of Gelfand pairs $(G(n), K(n))_\{n\ge 1\}$. By using the integral representation theory of G. Choquet on convex cones, we establish a Bochner type representation of any element $\varphi $ of the set $\{\mathcal\{P\}\}^\{\natural \}(G)$ of $K$-biinvariant continuous functions of positive type on $G$.},
affiliation = {Université Paul Verlaine-Metz Laboratoire de Mathématiques et Applications de Metz Bât. A Île de Saulcy 57045 Metz cedex 01 (France)},
author = {Rabaoui, Marouane},
journal = {Annales de l’institut Fourier},
keywords = {Function of positive type; Gelfand pair; Bochner-Godement theorem; spherical pair; inductive limit; Von Neumann algebra; function of positive type; von Neumann algebra},
language = {eng},
number = {5},
pages = {1551-1573},
publisher = {Association des Annales de l’institut Fourier},
title = {A Bochner type theorem for inductive limits of Gelfand pairs},
url = {http://eudml.org/doc/10356},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Rabaoui, Marouane
TI - A Bochner type theorem for inductive limits of Gelfand pairs
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 5
SP - 1551
EP - 1573
AB - In this article, we prove a generalisation of Bochner-Godement theorem. Our result deals with Olshanski spherical pairs $(G, K)$ defined as inductive limits of increasing sequences of Gelfand pairs $(G(n), K(n))_{n\ge 1}$. By using the integral representation theory of G. Choquet on convex cones, we establish a Bochner type representation of any element $\varphi $ of the set ${\mathcal{P}}^{\natural }(G)$ of $K$-biinvariant continuous functions of positive type on $G$.
LA - eng
KW - Function of positive type; Gelfand pair; Bochner-Godement theorem; spherical pair; inductive limit; Von Neumann algebra; function of positive type; von Neumann algebra
UR - http://eudml.org/doc/10356
ER -

References

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