Champs d'algèbres duales et algèbres duales uniformes d'opérateurs sur l'espace de Hilbert

Gilles Cassier

Studia Mathematica (1993)

  • Volume: 106, Issue: 2, page 101-119
  • ISSN: 0039-3223

Abstract

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In the first part of this work, we establish some general properties of dual algebras and of direct integral dual algebras. In the second part, we give a complete description of singly generated uniform dual algebras of operators.

How to cite

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Cassier, Gilles. "Champs d'algèbres duales et algèbres duales uniformes d'opérateurs sur l'espace de Hilbert." Studia Mathematica 106.2 (1993): 101-119. <http://eudml.org/doc/216006>.

@article{Cassier1993,
author = {Cassier, Gilles},
journal = {Studia Mathematica},
keywords = {dual algebras; direct integral dual algebras; singly generated uniform dual algebras of operators},
language = {fre},
number = {2},
pages = {101-119},
title = {Champs d'algèbres duales et algèbres duales uniformes d'opérateurs sur l'espace de Hilbert},
url = {http://eudml.org/doc/216006},
volume = {106},
year = {1993},
}

TY - JOUR
AU - Cassier, Gilles
TI - Champs d'algèbres duales et algèbres duales uniformes d'opérateurs sur l'espace de Hilbert
JO - Studia Mathematica
PY - 1993
VL - 106
IS - 2
SP - 101
EP - 119
LA - fre
KW - dual algebras; direct integral dual algebras; singly generated uniform dual algebras of operators
UR - http://eudml.org/doc/216006
ER -

References

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  1. [1] B. Beauzamy, Introduction to Operator Theory and Invariant Subspaces, North-Holland Math. Library, 1988. Zbl0663.47002
  2. [2] H. Bercovici, C. Foiaş and C. Pearcy, Dual Algebras with Applications to Invariant Subspaces and Dilation Theory, CBMS Regional Conf. Ser. in Math. 56, Amer. Math. Soc., 1985. Zbl0569.47007
  3. [3] G. Cassier, Algèbres duales uniformes d'opérateurs sur l'espace de Hilbert, Studia Math. 95 (1989), 17-32. Zbl0695.46019
  4. [4] G. Cassier, Sur la structure d'algèbres duales uniformes d'opérateurs sur l'espace de Hilbert, C. R. Acad. Sci. Paris Sér. I 309 (1989), 479-482. Zbl0678.47040
  5. [5] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, 1957. Zbl0088.32304
  6. [6] T. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. Zbl0213.40401
  7. [7] T. Gamelin and J. Garnett, Pointwise bounded approximation and Dirichlet algebras, J. Funct. Anal. 8 (1971), 360-404. Zbl0223.30056
  8. [8] F. Riesz et B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Gauthier-Villars, 1968. 
  9. [9] J. von Neumann, Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes, Math. Nachr. 4 (1951), 258-281. Zbl0042.12301

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