Closures of direct sums of classes of operators
HTML articles powered by AMS MathViewer
- by Don Hadwin PDF
- Proc. Amer. Math. Soc. 121 (1994), 697-701 Request permission
Abstract:
We prove that certain classes of Hilbert space operators that are direct sums of operators in specified classes are closed under sequential $\ast$-strong limits. One such example is the class of operators that are direct sums of operators that are either subnormal or have imaginary parts with spectrum contained in $[0,1] \cup [2,3]$.References
- Arlen Brown, Che Kao Fong, and Donald W. Hadwin, Parts of operators on Hilbert space, Illinois J. Math. 22 (1978), no. 2, 306–314. MR 500254
- 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
- John Ernest, Charting the operator terrain, Mem. Amer. Math. Soc. 6 (1976), no. 171, iii+207. MR 463941, DOI 10.1090/memo/0171
- Donald W. Hadwin, An asymptotic double commutant theorem for $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 244 (1978), 273–297. MR 506620, DOI 10.1090/S0002-9947-1978-0506620-0
- Donald W. Hadwin, Approximating direct integrals of operators by direct sums, Michigan Math. J. 25 (1978), no. 1, 123–127. MR 500245
- Donald W. Hadwin, Nonseparable approximate equivalence, Trans. Amer. Math. Soc. 266 (1981), no. 1, 203–231. MR 613792, DOI 10.1090/S0002-9947-1981-0613792-6
- Donald W. Hadwin, Completely positive maps and approximate equivalence, Indiana Univ. Math. J. 36 (1987), no. 1, 211–228. MR 876999, DOI 10.1512/iumj.1987.36.36011
- Donald W. Hadwin, Continuous functions of operators; a functional calculus, Indiana Univ. Math. J. 27 (1978), no. 1, 113–125. MR 467367, DOI 10.1512/iumj.1978.27.27010
- W. Forrest Stinespring, Positive functions on $C^*$-algebras, Proc. Amer. Math. Soc. 6 (1955), 211–216. MR 69403, DOI 10.1090/S0002-9939-1955-0069403-4
- Dan Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), no. 1, 97–113. MR 415338
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 697-701
- MSC: Primary 47D99; Secondary 46H15, 47A15, 47A20
- DOI: https://doi.org/10.1090/S0002-9939-1994-1209423-1
- MathSciNet review: 1209423