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Czasopismo
1997 | 122 | 2 | 183-193
Tytuł artykułu

The set of automorphisms of B(H) is topologically reflexive in B(B(H))

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence $(Φ_n)$ of automorphisms of B(H) (depending on A) such that $Φ(A)= lim_n Φ_n(A)$. Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).
Czasopismo
Rocznik
Tom
122
Numer
2
Strony
183-193
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-04-02
poprawiono
1996-09-06
Twórcy
  • Institute of Mathematics, Lajos Kossuth University, P.O. Box 12, 4010 Debrecen, Hungary, molnarl@math.klte.hu
Bibliografia
  • [Bre] M. Brešar, Characterizations of derivations on some normed algebras with involution, J. Algebra 152 (1992), 454-462.
  • [BS1] M. Brešar and P. Šemrl, Mappings which preserve idempotents, local automorphisms and local derivations, Canad. J. Math. 45 (1993), 483-496.
  • [BS2] M. Brešar and P. Šemrl, On local automorphisms and mappings that preserve idempotents, Studia Math. 113 (1995), 101-108.
  • [FMS] C. K. Fong, C. R. Miers and A. R. Sourour, Lie and Jordan ideals of operators on Hilbert space, Proc. Amer. Math. Soc. 84 (1982), 516-520.
  • [Her] I. N. Herstein, Jordan homomorphisms, Trans. Amer. Math. Soc. 81 (1956), 331-341.
  • [JR] N. Jacobson and C. Rickart, Jordan homomorphisms of rings, ibid. 69 (1950), 479-502.
  • [Kad1] R. V. Kadison, Isometries of operator algebras, Ann. of Math. 54 (1951), 325-338.
  • [Kad2] R. V. Kadison, Local derivations, J. Algebra 130 (1990), 494-509.
  • [LS] 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.
  • [LoS] A. I. Loginov and V. S. Shul'man, Hereditary and intermediate reflexivity of W*-algebras, Izv. Akad. Nauk SSSR 39 (1975), 1260-1273 (in Russian); English transl.: Math. USSR-Izv. 9 (1975), 1189-1201.
  • [Pal] T. W. Palmer, Banach Algebras and the General Theory of *-Algebras, Vol. I, Encyclopedia Math. Appl. 49, Cambridge University Press, 1994.
  • [PS] H. Porta and J. T. Schwartz, Representations of the algebra of all operators in Hilbert space, and related analytic function algebras, Comm. Pure Appl. Math. 20 (1967), 457-492.
  • [RD] B. Russo and H. A. Dye, A note on unitary operators in C*-algebras, Duke Math. J. 33 (1966), 413-416.
  • [Shu] V. S. Shul'man, Operators preserving ideals in C*-algebras, Studia Math. 109 (1994), 67-72.
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bwmeta1.element.bwnjournal-article-smv122i2p183bwm
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