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2009 | 7 | 3 | 479-486
Tytuł artykułu

A generalization of peripherally-multiplicative surjections between standard operator algebras

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EN
Abstrakty
EN
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A 1 TA 2 −1 and ϕ(T) = A 2 TA 1 −1 for some bijective bounded linear operators A 1; A 2 of X onto Y, or of the form φ(T) = B 1 T*B 2 −1 and ϕ(T) = B 2 T*B −1 for some bijective bounded linear operators B 1;B 2 of X* onto Y.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
3
Strony
479-486
Opis fizyczny
Daty
wydano
2009-09-01
online
2009-08-12
Twórcy
autor
Bibliografia
  • [1] Aupetit B., Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras, J. London Math. Soc., 2000, 62, 917–924 http://dx.doi.org/10.1112/S0024610700001514
  • [2] Aupetit B., du T. Mouton H., Spectrum preserving linear mappings in Banach algebras, Studia Math., 1994, 109, 91–100
  • [3] Brešar M., Šemrl P., Mappings which preserve idempotents, local automorphisms, and local derivations, Canad J. Math., 1993, 45, 483–496
  • [4] Brešar M., Šemrl P., Linear maps preserving the spectral radius, J. Funct. Anal., 1996, 142, 360–368 http://dx.doi.org/10.1006/jfan.1996.0153
  • [5] Cui J.-L., Hou J.-C., Additive maps on standard operator algebras preserving parts of the spectrum, J. Math. Anal. Appl., 2003, 282, 266–278 http://dx.doi.org/10.1016/S0022-247X(03)00146-X
  • [6] Hatori O., Hino K., Miura T., Oka H., Peripherally monomial-preserving maps between uniform algebras, Mediterr. J. Math., 2009, 6, 47–60 http://dx.doi.org/10.1007/s00009-009-0166-5
  • [7] Hatori O., Miura T., Oka H., An example of multiplicatively spectrum-preserving maps between non-isomorphic semi-simple commutative Banach algebras, Nihonkai Math. J., 2007, 18, 11–15
  • [8] Hatori O., Miura T., Takagi H., Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving property, Proc. Amer. Math. Soc., 2006, 134, 2923–2930 http://dx.doi.org/10.1090/S0002-9939-06-08500-5
  • [9] Hatori O., Miura T., Takagi H., Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative, J. Math. Anal. Appl., 2007, 326, 281–296 http://dx.doi.org/10.1016/j.jmaa.2006.02.084
  • [10] Hatori O., Miura T., Takagi H., Multiplicatively spectrum-preserving and norm-preserving maps between invertible groups of commutative Banach algebras, preprint
  • [11] Honma D., Surjections on the algebras of continuous functions which preserve peripheral spectrum, Contemp. Math., 2007, 435, 199–205
  • [12] Hou J.-C., Li C.-K., Wong N.-C., Jordan isomorphisms and maps preserving spectra of certain operator products, Studia Math., 2008, 184, 31–47 http://dx.doi.org/10.4064/sm184-1-2
  • [13] Jafarian A.A., Sourour A., Spectrum preserving linear maps, J. Funct. Anal., 1986, 66, 255–261 http://dx.doi.org/10.1016/0022-1236(86)90073-X
  • [14] Jiménez-Vargas A., Luttman A., Villegas-Vallecillos M., Weakly peripherally multiplicative surjections of pointed lipschitz algebras, preprint
  • [15] Lambert S., Luttman A., Tonev T., Weakly peripherally-multiplicative mappings between uniform algebras, Contemp. Math., 2007, 435, 265–281
  • [16] Luttman A., Lambert S., Norm conditions for uniform algebra isomorphisms, Cent. Eur. J. Math., 2008, 6, 272–280 http://dx.doi.org/10.2478/s11533-008-0016-x
  • [17] Luttman A., Tonev T., Uniform algebra isomorphisms and peripheral multiplicativity, Proc. Amer. Math. Soc., 2007, 135, 3589–3598 http://dx.doi.org/10.1090/S0002-9939-07-08881-8
  • [18] Miura T., Honma D., Shindo R., Divisibly norm-preserving maps between commutative Banach algebras, preprint
  • [19] Molnár L., Some characterizations of the automorphisms of B(H) and C(X), Proc. Amer. Math. Soc., 2001, 130, 111–120 http://dx.doi.org/10.1090/S0002-9939-01-06172-X
  • [20] Molnár L., Selected preserver problems on algebraic structures of linear operators and on function spaces, Lecture Notes in Math., Springer, 2006, 1895
  • [21] Rao N.V., Roy A.K., Multiplicatively spectrum-preserving maps of function algebras, Proc. Amer. Math. Soc., 2005, 133, 1135–1142 http://dx.doi.org/10.1090/S0002-9939-04-07615-4
  • [22] Rao N.V., Roy A.K., Multiplicatively spectrum-preserving maps of function algebras II, Proc. Edinburgh Math. Soc., 2005, 48, 219–229 http://dx.doi.org/10.1017/S0013091504000719
  • [23] Šemrl P., Two characterizations of automorphisms on B(X), Studia Math., 1993, 105, 143–149
  • [24] Tonev T., Luttman A., Algebra isomorphisms between standard operator algebras, Studia Math., 2009, 191, 163–170 http://dx.doi.org/10.4064/sm191-2-4
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0033-4
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