# On local automorphisms and mappings that preserve idempotents

Studia Mathematica (1995)

- Volume: 113, Issue: 2, page 101-108
- ISSN: 0039-3223

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topBrešar, Matej, and Šemrl, Peter. "On local automorphisms and mappings that preserve idempotents." Studia Mathematica 113.2 (1995): 101-108. <http://eudml.org/doc/216163>.

@article{Brešar1995,

abstract = {Let B(H) be the algebra of all bounded linear operators on a Hilbert space H. Automorphisms and antiautomorphisms are the only bijective linear mappings θ of B(H) with the property that θ(P) is an idempotent whenever P ∈ B(H) is. In case H is separable and infinite-dimensional, every local automorphism of B(H) is an automorphism.},

author = {Brešar, Matej, Šemrl, Peter},

journal = {Studia Mathematica},

keywords = {algebra of all bounded linear operators on a Hilbert space; antiautomorphisms; idempotent; local automorphism},

language = {eng},

number = {2},

pages = {101-108},

title = {On local automorphisms and mappings that preserve idempotents},

url = {http://eudml.org/doc/216163},

volume = {113},

year = {1995},

}

TY - JOUR

AU - Brešar, Matej

AU - Šemrl, Peter

TI - On local automorphisms and mappings that preserve idempotents

JO - Studia Mathematica

PY - 1995

VL - 113

IS - 2

SP - 101

EP - 108

AB - Let B(H) be the algebra of all bounded linear operators on a Hilbert space H. Automorphisms and antiautomorphisms are the only bijective linear mappings θ of B(H) with the property that θ(P) is an idempotent whenever P ∈ B(H) is. In case H is separable and infinite-dimensional, every local automorphism of B(H) is an automorphism.

LA - eng

KW - algebra of all bounded linear operators on a Hilbert space; antiautomorphisms; idempotent; local automorphism

UR - http://eudml.org/doc/216163

ER -

## References

top- [1] L. B. Beasley and N. J. Pullman, Linear operators preserving idempotent matrices over fields, Linear Algebra Appl. 146 (1991), 7-20. Zbl0718.15004
- [2] M. Brešar, Characterizations of derivations on some normed algebras with involution, J. Algebra 152 (1992), 454-462. Zbl0769.16015
- [3] M. Brešar and P. Šemrl, Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483-496. Zbl0796.15001
- [4] G. H. Chan, M. H. Lim and K. K. Tan, Linear preservers on matrices, Linear Algebra Appl. 93 (1987), 67-80. Zbl0619.15003
- [5] P. R. Chernoff, Representations, automorphisms and derivations of some operator algebras, J. Funct. Anal. 12 (1973), 275-289. Zbl0252.46086
- [6] M. Eidelheit, On isomorphisms of rings of linear operators, Studia Math. 9 (1940), 97-105. Zbl0061.25301
- [7] I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1969. Zbl0232.16001
- [8] N. Jacobson and C. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479-502. Zbl0039.26402
- [9] A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. Zbl0589.47003
- [10] R. V. Kadison, Local derivations, J. Algebra 130 (1990), 494-509. Zbl0751.46041
- [11] D. R. Larson and A. R. Sourour, Local derivations and local automorphisms of B(X), in: Proc. Sympos. Pure Math. 51, Part 2, Providence, R.I., 1990, 187-194. Zbl0713.47045
- [12] C. Pearcy and D. Topping, Sums of small numbers of idempotents, Michigan Math. J. 14 (1967), 453-465.

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