A note on local automorphisms

Ajda Fošner

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 981-986
  • ISSN: 0011-4642

Abstract

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Let H be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of ( H ) , the algebra of all bounded linear operators on a Hilbert space H , is an automorphism.

How to cite

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Fošner, Ajda. "A note on local automorphisms." Czechoslovak Mathematical Journal 56.3 (2006): 981-986. <http://eudml.org/doc/31084>.

@article{Fošner2006,
abstract = {Let $H$ be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of $\mathcal \{B\}(H)$, the algebra of all bounded linear operators on a Hilbert space $H$, is an automorphism.},
author = {Fošner, Ajda},
journal = {Czechoslovak Mathematical Journal},
keywords = {automorphism; local automorphism; algebra of operators on a Hilbert space; automorphism; local automorphism; algebra of operators on a Hilbert space},
language = {eng},
number = {3},
pages = {981-986},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on local automorphisms},
url = {http://eudml.org/doc/31084},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Fošner, Ajda
TI - A note on local automorphisms
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 981
EP - 986
AB - Let $H$ be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of $\mathcal {B}(H)$, the algebra of all bounded linear operators on a Hilbert space $H$, is an automorphism.
LA - eng
KW - automorphism; local automorphism; algebra of operators on a Hilbert space; automorphism; local automorphism; algebra of operators on a Hilbert space
UR - http://eudml.org/doc/31084
ER -

References

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  2. 10.4064/sm-9-1-97-105, Studia Math. 9 (1940), 97–105. (1940) Zbl0061.25301MR0004725DOI10.4064/sm-9-1-97-105
  3. 10.4153/CJM-1984-048-x, Canad. J.  Math. 36 (1984), 820–829. (1984) MR0762744DOI10.4153/CJM-1984-048-x
  4. 10.1090/S0002-9947-1950-0038335-X, Trans. Amer. Math. Soc. 69 (1950), 479–502. (1950) MR0038335DOI10.1090/S0002-9947-1950-0038335-X
  5. Local derivations and local automorphisms of  B ( X ) , Proc. Symp. Pure Math. 51 (1990), 187–194. (1990) MR1077437
  6. 10.1307/mmj/1028999848, Michigan Math.  J. 14 (1967), 453–465. (1967) MR0218922DOI10.1307/mmj/1028999848

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