PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2010 | 8 | 1 | 135-147
Tytuł artykułu

Norm conditions for real-algebra isomorphisms between uniform algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let A and B be uniform algebras. Suppose that α ≠ 0 and A 1 ⊂ A. Let ρ, τ: A 1 → A and S, T: A 1 → B be mappings. Suppose that ρ(A 1), τ(A 1) and S(A 1), T(A 1) are closed under multiplications and contain expA and expB, respectively. If ‖S(f)T(g) − α‖∞ = ‖ρ(f)τ(g) − α‖∞ for all f, g ∈ A 1, S(e 1)−1 ∈ S(A 1) and S(e 1) ∈ T(A 1) for some e 1 ∈ A 1 with ρ(e 1) = 1, then there exists a real-algebra isomorphism $$ \tilde S $$: A → B such that $$ \tilde S $$(ρ(f)) = S(e 1)−1 S(f) for every f ∈ A 1. We also give some applications of this result.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
1
Strony
135-147
Opis fizyczny
Daty
wydano
2010-02-01
online
2010-02-02
Twórcy
autor
Bibliografia
  • [1] Browder A., Introduction to function algebras, W.A. Benjamin, 1969
  • [2] 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
  • [3] 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
  • [4] Hatori O., Miura T., Takagi H., Multiplicatively spectrum-preserving and norm-preserving maps between invertible groups of commutative Banach algebras, preprint.
  • [5] Hatori O., Hino K., Miura T., Oka H., Peripherally monomial-preserving maps between uniform algebras, Mediterr. J. Math., 2009, 6, 47–59 http://dx.doi.org/10.1007/s00009-009-0166-5
  • [6] Hatori O., Miura T., Shindo R., Takagi H., Generalizations of spectrally multiplicative surjections between uniform algebras, preprint
  • [7] Honma D., Surjections on the algebras of continuous functions which preserve peripheral spectrum, Contemp. Math., 2006,435, 199–205
  • [8] Honma D., Norm-preserving surjections on algebras of continuous functions, Rocky Mountain J. Math., to appear
  • [9] Kelley J.L., General topology, D. Van Nostrand Company (Canada), 1955
  • [10] Lambert S., Luttman A., Tonev T., Weakly peripherally-multiplicative mappings between uniform algebras, Contemp. Math., 2007, 435, 265–281
  • [11] 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
  • [12] Luttman A., Lambert S., Norm conditions for uniform algebra isomorphisms, Cent. Eur. J. Math., 2008, 6(2), 272–280 http://dx.doi.org/10.2478/s11533-008-0016-x
  • [13] Miura T., Honma D., Shindo R., Divisibly norm-preserving maps between commutative Banach algebras, Rocky Mountain J. Math., to appear
  • [14] 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
  • [15] 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
  • [16] 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
  • [17] Shindo R., Maps between uniform algebras preserving norms of rational functions, preprint
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0060-1
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.