Non-commutative Gelfand-Naimark theorem

Janusz Migda

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 253-255
  • ISSN: 0010-2628

Abstract

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We show that if Y is the Hausdorffization of the primitive spectrum of a C * -algebra A then A is * -isomorphic to the C * -algebra of sections vanishing at infinity of the canonical C * -bundle over Y .

How to cite

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Migda, Janusz. "Non-commutative Gelfand-Naimark theorem." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 253-255. <http://eudml.org/doc/247488>.

@article{Migda1993,
abstract = {We show that if Y is the Hausdorffization of the primitive spectrum of a $C^\{\ast \}$-algebra $A$ then $A$ is $\ast $-isomorphic to the $C^\{\ast \}$-algebra of sections vanishing at infinity of the canonical $C^\{\ast \}$-bundle over $Y$.},
author = {Migda, Janusz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$C^\{\ast \}$-algebra; $C^\{\ast \}$-bundle; sectional representation; -bundle; sectional representation; primitive spectrum of a -algebra},
language = {eng},
number = {2},
pages = {253-255},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Non-commutative Gelfand-Naimark theorem},
url = {http://eudml.org/doc/247488},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Migda, Janusz
TI - Non-commutative Gelfand-Naimark theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 253
EP - 255
AB - We show that if Y is the Hausdorffization of the primitive spectrum of a $C^{\ast }$-algebra $A$ then $A$ is $\ast $-isomorphic to the $C^{\ast }$-algebra of sections vanishing at infinity of the canonical $C^{\ast }$-bundle over $Y$.
LA - eng
KW - $C^{\ast }$-algebra; $C^{\ast }$-bundle; sectional representation; -bundle; sectional representation; primitive spectrum of a -algebra
UR - http://eudml.org/doc/247488
ER -

References

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  1. Dauns J., Hofmann K.H., Representation of rings by sections, Mem. Amer. Math. Soc. 83 (1968). (1968) Zbl0174.05703MR0247487
  2. Dixmier J., Les C * -algèbres et leurs representations, Gauthier-Villars, Paris, 1969. Zbl0288.46055MR0246136
  3. Dupre M.J., Gillette M.R., Banach bundles, Banach modules and automorphisms of C * - algebras, Research Notes in Math. 92, Pitman Advanced Publishing Program, Boston- London-Melbourne, 1983. Zbl0536.46048MR0721812
  4. Fell J.M.G., The structure of algebras of operator fields, Acta Math. 106 (1961), 233-280. (1961) Zbl0101.09301MR0164248
  5. Fell J.M.G., An extension of Macley’s method to Banach * -algebraic bundles, Mem. Amer. Math. Soc. 90 (1969). (1969) MR0259619
  6. Tomiyama J., Topological representations of C * -algebras, Tohôku Math. J. 14 (1962), 187-204. (1962) MR0143053

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