Commutative subalgebras of the corona
HTML articles powered by AMS MathViewer
- by Dan Kucerovsky PDF
- Proc. Amer. Math. Soc. 132 (2004), 3027-3034 Request permission
Abstract:
We use methods of noncommutative functional analysis to extend the range of the usual functional calculus, for certain subalgebras of the corona. In particular, we construct corona projections with interesting properties.References
- L. G. Brown, R. G. Douglas, and P. A. Fillmore, Unitary equivalence modulo the compact operators and extensions of $C^{\ast }$-algebras, Proceedings of a Conference on Operator Theory (Dalhousie Univ., Halifax, N.S., 1973) Lecture Notes in Math., Vol. 345, Springer, Berlin, 1973, pp. 58–128. MR 0380478
- Robert C. Busby, Double centralizers and extensions of $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 132 (1968), 79–99. MR 225175, DOI 10.1090/S0002-9947-1968-0225175-5
- Don Deckard and Carl Pearcy, On algebraic closure in function algebras, Proc. Amer. Math. Soc. 15 (1964), 259–263. MR 161171, DOI 10.1090/S0002-9939-1964-0161171-6
- Don Deckard and Carl Pearcy, On continuous matrix-valued functions on a Stonian space, Pacific J. Math. 14 (1964), 857–869. MR 172130, DOI 10.2140/pjm.1964.14.857
- George A. Elliott and Dan Kucerovsky, An abstract Voiculescu-Brown-Douglas-Fillmore absorption theorem, Pacific J. Math. 198 (2001), no. 2, 385–409. MR 1835515, DOI 10.2140/pjm.2001.198.385
- Dwight B. Goodner, The closed convex hull of certain extreme points, Proc. Amer. Math. Soc. 15 (1964), 256–258. MR 163152, DOI 10.1090/S0002-9939-1964-0163152-5
- G. G. Kasparov, Hilbert $C^{\ast }$-modules: theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), no. 1, 133–150. MR 587371
- G. G. Kasparov, The operator $K$-functor and extensions of $C^{\ast }$-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), no. 3, 571–636, 719 (Russian). MR 582160
- Jacob v. B. Hjelmborg and Mikael Rørdam, On stability of $C^*$-algebras, J. Funct. Anal. 155 (1998), no. 1, 153–170. MR 1623142, DOI 10.1006/jfan.1997.3221
- I. I. Parovičenko, On a universal bicompactum of weight $\aleph$, Dokl. Akad. Nauk SSSR 150 (1963), 36–39. MR 0150732
- Gert K. Pedersen, The corona construction, Operator Theory: Proceedings of the 1988 GPOTS-Wabash Conference (Indianapolis, IN, 1988) Pitman Res. Notes Math. Ser., vol. 225, Longman Sci. Tech., Harlow, 1990, pp. 49–92. MR 1075635
- Dan Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), no. 1, 97–113. MR 415338
- Russell C. Walker, The Stone-Čech compactification, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 83, Springer-Verlag, New York-Berlin, 1974. MR 0380698, DOI 10.1007/978-3-642-61935-9
- R. Grant Woods, Co-absolutes of remainders of Stone-Čech compactifications, Pacific J. Math. 37 (1971), 545–560. MR 307179, DOI 10.2140/pjm.1971.37.545
Additional Information
- Dan Kucerovsky
- Affiliation: Department of Mathematics and Statistics, University of New Brunswick- Fredericton, Fredericton, New Brunswick, Canada E3B 5A3
- Email: dkucerov@unb.ca
- Received by editor(s): April 16, 2003
- Published electronically: May 12, 2004
- Additional Notes: This research was supported by NSERC, under grant # 228065–00
- Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3027-3034
- MSC (2000): Primary 46L85; Secondary 47A60, 46L80
- DOI: https://doi.org/10.1090/S0002-9939-04-07548-3
- MathSciNet review: 2063124