Download PDF - Accretive approximation in C*-algebrasAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Accretive approximation in C*-algebras

Authors 1

Affiliations

  1. Mathematisches Institut der WWU Münster, Einsteinstr. 62, 48149 Münster, Germany

Abstract

The problem of approximation by accretive elements in a unital C*-algebra suggested by P. R. Halmos is substantially solved. The key idea is the observation that accretive approximation can be regarded as a combination of positive and self-adjoint approximation. The approximation results are proved both in the C*-norm and in another, topologically equivalent norm.

Bibliography

  1. [Be 1] R. Berntzen, Normal spectral approximation in C*-algebras and in von Neumann algebras, Rend. Circ. Mat. Palermo, to appear.
  2. [Be 2] R. Berntzen, Extreme points in the set of normal spectral approximants, Acta Sci. Math. (Szeged) 59 (1994), 143-160.
  3. [Be 3] R. Berntzen, Spectral approximation of normal operators, ibid., to appear.
  4. [Bo 1] R. Bouldin, Positive approximants, Trans. Amer. Math. Soc. 177 (1973), 391-403.
  5. [Bo 2] R. Bouldin, Operators with a unique positive near-approximant, Indiana Univ. Math. J. 23 (1973), 421-427.
  6. [Bo 3] R. Bouldin, Self-adjoint approximants, ibid. 27 (1978), 299-307.
  7. [Ha] P. R. Halmos, Positive approximants of operators, ibid. 21 (1972), 951-960.
  8. [Pe] G. K. Pedersen, C*-Algebras and Their Automorphism Groups, London Math. Soc. Monographs 13, Academic Press, London, 1989.
  9. [Val] F. A. Valentine, Convex Sets, McGraw-Hill, New York, 1964.
Studia Mathematica
1995-1996/117/2
Export to PBN, Opens in new tab
Pages:
115-121
Main language of publication
English
Received
1994-12-27
Published
1996
Exact and natural sciences