On local automorphisms and mappings that preserve idempotents

Matej Brešar; Peter Šemrl

Studia Mathematica (1995)

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

Abstract

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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.

How to cite

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Brešar, 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

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  9. [9] A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. Zbl0589.47003
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