Approximate topology on $\textrm {Rep}(A)$
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- by Sa Ge Lee
- Proc. Amer. Math. Soc. 86 (1982), 461-463
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671216-3
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Abstract:
Let $A$ be a ${C^*}$-algebra and Rep$(A)$ the set of all nondegenerate representations of $A$. We define a new topology on Rep$(A)$ and study the relations with the point weak topology of Rep$(A)$.References
- William Arveson, Notes on extensions of $C^{^*}$-algebras, Duke Math. J. 44 (1977), no. 2, 329–355. MR 438137 N. Bourbaki, General topology, Part 1, Hermann, Paris, 1966 (English transl., Addison-Wesley, Reading, Mass., 1966).
- Jacques Dixmier, $C^*$-algebras, North-Holland Mathematical Library, Vol. 15, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Translated from the French by Francis Jellett. MR 0458185
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- L. Terrell Gardner, On the “third definition” of the topology on the spectrum of a $C^{\ast }$-algebra, Canadian J. Math. 23 (1971), 445–450. MR 281011, DOI 10.4153/CJM-1971-047-1 D. W. Hadwin, Approximate equivalence and completely positive maps (preprint).
- Donald W. Hadwin, An operator-valued spectrum, Indiana Univ. Math. J. 26 (1977), no. 2, 329–340. MR 428089, DOI 10.1512/iumj.1977.26.26025
- Warren Page, Topological uniform structures, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 515583
- Zirô Takeda, Conjugate spaces of operator algebras, Proc. Japan Acad. 30 (1954), 90–95. MR 63578
- Masamichi Takesaki, A duality in the representation theory of $C^{\ast }$-algebras, Ann. of Math. (2) 85 (1967), 370–382. MR 209859, DOI 10.2307/1970350
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 461-463
- MSC: Primary 46L05; Secondary 46K10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671216-3
- MathSciNet review: 671216