Algebras with involution with linear codimension growth

Normed algebras with involution

We show that most of the theory of Hermitian Banach algebras can be proved for normed ∗-algebras without the assumption of completeness. The condition r(x) ≤ p(x) for all x (where p(x) = r(x∗x)1/2 is the Pták function), which is essential in the theory of Hermitian Banach algebras, is replaced for normed ∗-algebras by the condition r(x + y) ≤ p(x) + p(y) for all x, y. In case of Banach ∗-algebr...

Generic Algebras with Involution Of

Codimension 1 Linear Isometries on Function Algebras

Let A be a function algebra on a locally compact Hausdorff space. A linear isometry T : A −→ A is said to be of codimension 1 if the range of T has codimension 1 in A. In this paper, we provide and study a classification of codimension 1 linear isometries on function algebras in general and on Douglas algebras in particular.

2-local Mappings on Algebras with Involution

We investigate 2-local ∗-automorphisms, 2-local ∗-antiautomorphisms, and 2-local Jordan ∗-derivations on certain algebras with involution.

ALGEBRAIC ALGEBRAS WITH INVOLUTION susan montgomery

The following theorem is proved: Let R be an algebra with involution over an uncountable field F. Then if the symmetric elements of R are algebraic, R is algebraic. In this paper we consider the following question: "Let R be an algebra with involution over a field F, and assume that the symmetric elements S of R are algebraic over F. Is R algebraic over FT* Previous results related to this ques...