Approximately order zero maps between C?-algebras

APPROXIMATELY INNER sigma-DYNAMICS ON C* ALGEBRAS

A class of certain properties of approximately n-multiplicative maps between locally multiplicatively convex algebras

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

Invertibility-preserving Maps of C∗-algebras with Real Rank Zero

In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras andΦ : A→ B is a linear map onto B that preserves the spectrum of elements, thenΦ is a Jordan isomorphism if either A or B is a C∗-al...

Completely Contractive Maps between C∗-algebras

We said that φ is n-positive if φn is positive and that φ is completely positive if φn is positive for all n. The map φ is said to be n-bounded (resp., n-contractive) if ‖φn‖ ≤ c (resp., ‖φn‖ ≤ 1). The map φ is said to be completely bounded (resp., completely contractive) if ‖φ‖cb = supn‖φ‖n <∞ (resp., ‖φ‖cc = supn‖φn‖ ≤ 1). npositivity (resp., n-boundedness or n-contractivity) implies (n−1)-po...

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.