Accretive approximation in C*-algebras

• Autorzy: Reiner Berntzen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A58: Operator approximation theory
• 47B44: Accretive operators, dissipative operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995-1996
• Tom: 117
• Numer: 2
• Strony: 115-121

Daty

wydano

1996

otrzymano

1994-12-27

Twórcy

autor

Reiner Berntzen

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

Bibliografia

• [Be 1] R. Berntzen, Normal spectral approximation in C*-algebras and in von Neumann algebras, Rend. Circ. Mat. Palermo, to appear.
• [Be 2] R. Berntzen, Extreme points in the set of normal spectral approximants, Acta Sci. Math. (Szeged) 59 (1994), 143-160.
• [Be 3] R. Berntzen, Spectral approximation of normal operators, ibid., to appear.
• [Bo 1] R. Bouldin, Positive approximants, Trans. Amer. Math. Soc. 177 (1973), 391-403.
• [Bo 2] R. Bouldin, Operators with a unique positive near-approximant, Indiana Univ. Math. J. 23 (1973), 421-427.
• [Bo 3] R. Bouldin, Self-adjoint approximants, ibid. 27 (1978), 299-307.
• [Ha] P. R. Halmos, Positive approximants of operators, ibid. 21 (1972), 951-960.
• [Pe] G. K. Pedersen, C*-Algebras and Their Automorphism Groups, London Math. Soc. Monographs 13, Academic Press, London, 1989.
• [Val] F. A. Valentine, Convex Sets, McGraw-Hill, New York, 1964.