# Accretive approximation in C*-algebras

Studia Mathematica (1996)

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

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topBerntzen, 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

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

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