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1996 | 69 | 2 | 157-165
Tytuł artykułu

The closure of the invertibles in a von Neumann algebra

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results, namely Feldman and Kadison's characterization of the closure of the invertibles in a von Neumann algebra and a more recent characterization of the closure of the invertibles in the bounded linear operators on a Hilbert space.
Słowa kluczowe
Rocznik
Tom
69
Numer
2
Strony
157-165
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-07-04
Twórcy
  • Dipartimento di Matematica, università di Genova, via Dodecaneso 35, 16146 Genova, Italy
autor
  • Queen's University, Belfast BT7 1NN, Northern Ireland, UK
Bibliografia
  • [1] R. Bouldin, The essential minimum modulus, Indiana Univ. Math. J. 30 (1981), 513-517.
  • [2] R. Bouldin, Closure of the invertible operators in Hilbert space, Proc. Amer. Math. Soc. 108 (1990), 721-726.
  • [3] R. Bouldin, Approximating Fredholm operators on a nonseparable Hilbert space, Glasgow Math. J. 35 (1993), 167-178.
  • [4] L. Burlando, On continuity of the spectral radius function in Banach algebras, Ann. Mat. Pura Appl. (4) 156 (1990), 357-380.
  • [5] L. Burlando, Distance formulas on operators whose kernel has fixed Hilbert dimension, Rend. Mat. (7) 10 (1990), 209-238.
  • [6] L. Burlando, Approximation by semi-Fredholm and semi-α-Fredholm operators in Hilbert spaces of arbitrary dimension, to appear.
  • [7] G. Edgar, J. Ernest and S. G. Lee, Weighing operator spectra, Indiana Univ. Math. J. 21 (1971), 61-80.
  • [8] J. Feldman and R. V. Kadison, The closure of the regular operators in a ring of operators, Proc. Amer. Math. Soc. 5 (1954), 909-916.
  • [9] C. W. Groetsch, Representations of the generalized inverse, J. Math. Anal. Appl. 49 (1975), 154-157.
  • [10] R. E. Harte, Regular boundary elements, Proc. Amer. Math. Soc. 99 (1987), 328-330.
  • [11] R. E. Harte, Invertibility and Singularity for Bounded Linear Operators, Dekker, New York, 1988.
  • [12] R. E. Harte and M. Mbekhta, On generalized inverses in C*-algebras, Studia Math. 103 (1992), 71-77.
  • [13] R. E. Harte and M. Mbekhta, Generalized inverses in C*-algebras II, ibid. 106 (1993), 129-138.
  • [14] R. E. Harte and M. Ó Searcóid, Positive elements and the B* condition, Math. Z. 193 (1986), 1-9.
  • [15] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
  • [16] G. J. Murphy, C*-algebras and Operator Theory, Academic Press, 1990.
  • [17] C. Olsen, Unitary approximation, J. Funct. Anal. 85 (1989), 392-419.
  • [18] G. K. Pedersen, Unitary extension and polar decomposition in a C*-algebra, J. Operator Theory 17 (1987), 357-364.
  • [19] S. Sakai, C*-algebras and W*-algebras, Springer, New York, 1971.
  • [20] J. Weidmann, Linear Operators in Hilbert Spaces, Springer, New York, 1980.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv69i2p157bwm
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