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Voiculescu Theorem, Sobolev Lemma, and Extensions of smooth algebras
Author(s):
Xiaolu
Wang
Journal:
Bull. Amer. Math. Soc.
27
(1992),
292-297.
MSC (1991):
Primary 46L80;
Secondary 47B10, 19K33, 47B10, 46L87, 46J15, 46M20
MathSciNet review:
1161277
Retrieve article in:
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References |
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Additional information
References:
- [A1]
- M. F. Atiyah, Global theory of elliptic operators, Proc. Int. Conf. Funct. Anal. and Related Topics, Univ. Tokyo Press, Tokyo, 1970, pp.~21--23. MR 266247
- [A2]
- M. F. Atiyah, \emph{A survey of $K$-theory} vol.~575, Springer-Verlag, New York, 1977 pp.~1--9. MR 474299
- [Ar]
- W. Arveson, Notes on extensions of $C^*$-algebras, Duke Math J. \textbf{44} (1977), 329--355. MR 438137
- [B]
- F. A. Berezin, Quantization, Izv. Akad. Nauk SSSR Ser. Math. \textbf{38} (1974), 1109--1165. MR 395610
- [Bg]
- I. D. Berg, An extension of the Weyl-von Neumann theorem to normal operators, Trans. Amer. Math. Soc. \textbf{160} (1971), 365--371. MR 283610
- [B-C]
- C. A. Berger and L. A. Coburn, Toeplitz operators and quantum mechanics, J. Funct. Anal. \textbf{68} (1986), 273--299. MR 859136
- [BC]
- B. Blackadar and J. Cuntz, Differential Banach algebra norms and smooth subalgebras of $C^*$-algebras, preprint. MR 1225517
- [BDF]
- L. Brown, R. Douglas, and P. Fillmore, Extensions of $C^*$-algebras and $K$-homology, Ann. of Math. (2) \textbf{105} (1977), 265--324. MR 458196
- [CP]
- R. Carey and J. D. Pincus, Almost commuting algebras, $K$-theory and operator algebras, Lecture Notes in Math. vol. 575, Springer-Verlag, New York, 1977, pp. 19--43. MR 512491
- [C]
- A. Connes, Noncommutative differential geometry. \rm I, II, Inst. Hautes \'Etudes Sci. Publ. Math. \textbf{62} (1986), 257--360. MR 823176
- [CK]
- A. Connes and M. Karoubi, Caract\`er multiplicatif d'un module de Fredholm, C. R. Acad. Sci. Paris S\'er. I. Math. \textbf{299} (1984), 963--968. MR 774679
- [D]
- R. Douglas, On the smoothness of elements of Ext, Topics in modern operator theory, Birkhauser, 1981, pp.~63--69. MR 672816
- [DV]
- R. Douglas and D. Voiculescu, On the smoothness of sphere extensions, J. Operator Theory {\bf 6} (1981), 103--111. MR 637004
- [E]
- E. Effros, Advances in quantized functional calculus, Proc. I.C.M. (1986), 906--916. MR 934293
- [G]
- G. Gong, Smooth extensions for a finite $CW$-complex, Bull. Amer. Math. Soc. (N.S.) \textbf{22} (1990), 73--78. MR 1003863
- [HH]
- J. W. Helton and R. Howe, Integral Operators: commutators, traces, index, and homology, Lecture Notes in Math. vol. 345, Springer-Verlag, New York, 1973, pp., 141--209. MR 390829
- [Km]
- J. Kaminker, Pseudo-differential operators and differential structures. \rm II, Amer. J. Math. (1986), 703--718. MR 844636
- [K]
- G. Kasparov, The operator $K$-functor and extensions of $C^*$-algebras, Izv. Akad. Nauk SSSR Ser. Math. \textbf{44} (1980), 571--636. MR 582160
- [P]
- A. Pietsch, Operator Ideals, {\rm North-Holland, Amsterdam}, 1980. MR 582655
- [Sl]
- N. Salinas, Smooth extensions and smooth joint quasitriangularity, Oper. Theory: Adv. Appl. vol. 11, Birkhauser Baseland, Boston, 1983, pp., 303--332. MR 789646
- [S]
- W. F. Stinespring, Positive functions on $C^*$-algebras, Proc. Amer. Math. Soc. \textbf{6} (1955), 211--216. MR 69403
- [V1]
- D. Voiculescu, A noncommutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. \textbf{21} (1976), 97--113. MR 415338
- [V2]
- D. Voiculescu, Some results on norm-ideal perturbations of Hilbert space operators, J. Operator Theory \textbf{2} (1979), 30-37. MR 553861
- [W1]
- X. Wang, $KK$-theories for topological algebras, $K$-{\rm theory} \textbf{5} (1991), 97--150. MR 1140899
- [W2]
- X. Wang, Theorems of Voiculescu and Stinespring; Extensions of smooth algebras. MR
- [W3]
- X. Wang, Smooth extensions and quantized Fr\'echet algebras dimensions {\rm 0} and {\rm 1}. MR
- [W4]
- X. Wang, Quantizations, quantized smooth manifolds and invariants, Proc. NATO conference. MR
- [W5]
- X. Wang, Smooth $K$-homology, Chern character, and a noncommutative Sobolev Lemma, in preparation. MR
- [W6]
- X. Wang, Geometric BRST quantization and smooth Toeplitz extensions, in preparation. MR
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Additional Information:
DOI:
10.1090/S0273-0979-1992-00326-9
PII:
S 0273-0979(1992)00326-9
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