Spectrum preserving linear mappings in Banach algebras
نویسندگان
چکیده
منابع مشابه
Spectrum Preserving Linear Maps Between Banach Algebras
In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.
متن کاملInvertibility Preserving Linear Maps of Banach Algebras
This talk discusses a conjecture of R. V. Kadison and myself. Our conjecture is that each one-to-one linear map of one unital C*-algebra onto another that preserves the identity is a Jordan isomorphism if it maps the invertible elements of the first C*-algebra onto the invertible elements of the other C*-algebra. Connections are shown between this conjecture and Cartan’s uniqueness theorem. 1. ...
متن کاملPolynomially Spectrum-preserving Maps between Commutative Banach Algebras
Let A and B be unital semi-simple commutative Banach algebras. In this paper we study two-variable polynomials p which satisfy the following property: a map T from A onto B such that the equality σ(p(Tf, T g)) = σ(p(f, g)), f, g ∈ A holds is an algebra isomorphism.
متن کاملProjective Spectrum in Banach Algebras
For a tuple A = (A0, A1, ..., An) of elements in a unital Banach algebra B, its projective spectrum p(A) is defined to be the collection of z = [z0, z1, ..., zn] ∈ P such that A(z) = z0A0 + z1A1 + · · · + znAn is not invertible in B. The pre-image of p(A) in Cn+1 is denoted by P (A). When B is the k × k matrix algebra Mk(C), the projective spectrum is a projective hypersurface. In infinite dime...
متن کاملMultiplicatively Spectrum-preserving and Norm-preserving Maps between Invertible Groups of Commutative Banach Algebras
Let A and B be unital semisimple commutative Banach algebras and T a map from the invertible group A onto B. Linearity and multiplicativity of the map are not assumed. We consider the hypotheses on T : (1) σ(TfTg) = σ(fg); (2) σπ(TfTg−α)∩σπ(fg−α) 6= ∅; (3) r(TfTg−α) = r(fg−α) hold for some non-zero complex number α and for every f, g ∈ A, where σ(·) (resp. σπ(·)) denotes the (resp. peripheral) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1994
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-109-1-91-100