Accretive approximation in C*-algebras

Reiner Berntzen

Studia Mathematica (1996)

  • Volume: 117, Issue: 2, page 115-121
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Berntzen, Reiner. "Accretive approximation in C*-algebras." Studia Mathematica 117.2 (1996): 115-121. <http://eudml.org/doc/216246>.

@article{Berntzen1996,
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.},
author = {Berntzen, Reiner},
journal = {Studia Mathematica},
keywords = {approximation by accretive elements; unital -algebra; accretive approximation; combination of positive and selfadjoint approximation; -norm; topologically equivalent norm},
language = {eng},
number = {2},
pages = {115-121},
title = {Accretive approximation in C*-algebras},
url = {http://eudml.org/doc/216246},
volume = {117},
year = {1996},
}

TY - JOUR
AU - Berntzen, Reiner
TI - Accretive approximation in C*-algebras
JO - Studia Mathematica
PY - 1996
VL - 117
IS - 2
SP - 115
EP - 121
AB - 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.
LA - eng
KW - approximation by accretive elements; unital -algebra; accretive approximation; combination of positive and selfadjoint approximation; -norm; topologically equivalent norm
UR - http://eudml.org/doc/216246
ER -

References

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  1. [Be 1] R. Berntzen, Normal spectral approximation in C*-algebras and in von Neumann algebras, Rend. Circ. Mat. Palermo, to appear. Zbl0851.46039
  2. [Be 2] R. Berntzen, Extreme points in the set of normal spectral approximants, Acta Sci. Math. (Szeged) 59 (1994), 143-160. Zbl0802.47012
  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. Zbl0264.47020
  5. [Bo 2] R. Bouldin, Operators with a unique positive near-approximant, Indiana Univ. Math. J. 23 (1973), 421-427. Zbl0269.47010
  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. Zbl0263.47018
  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. 

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