Ideal and representation theory of the -algebra of a group with polynomial growth
Ideally factored algebras.
Idempotents dans les algèbres de Banach
Using the holomorphic functional calculus we give a characterization of idempotent elements commuting with a given element in a Banach algebra.
Incomplete normed algebra norms on Banach algebras
Induced bornological representations of bornological algebras
Inductive limits and tensor products of ordered topological vector spaces and algebras
Inequalities for exponentials in Banach algebras
For commuting elements x, y of a unital Banach algebra ℬ it is clear that . On the order hand, M. Taylor has shown that this inequality remains valid for a self-adjoint operator x and a skew-adjoint operator y, without the assumption that they commute. In this paper we obtain similar inequalities under conditions that lie between these extremes. The inequalities are used to deduce growth estimates of the form for all , where and c, s are constants.
Infinite -tensor product algebras.
Injective semigroup-algebras
Semigroups S for which the Banach algebra is injective are investigated and an application to the work of O. Yu. Aristov is described.
Inner amenability of Lau algebras
A concept of amenability for an arbitrary Lau algebra called inner amenability is introduced and studied. The inner amenability of a discrete semigroup is characterized by the inner amenability of its convolution semigroup algebra. Also, inner amenable Lau algebras are characterized by several equivalent statements which are similar analogues of properties characterizing left amenable Lau algebras.
Integral representations of the -Drazin inverse in -algebras
The paper gives new integral representations of the -Drazin inverse of an element of a -algebra that require no restriction on the spectrum of . The representations involve powers of and of its adjoint.
Invertibility in tensor products of Q-algebras
We consider, using various tensor norms, the completed tensor product of two unital lmc algebras one of which is commutative. Our main result shows that when the tensor product of two Q-algebras is an lmc algebra, then it is a Q-algebra if and only if pointwise invertibility implies invertibility (as in the Gelfand theory). This is always the case for Fréchet algebras.
Invertibility preserving linear mappings into M₂(ℂ)
We study discontinuous invertibility preserving linear mappings from a Banach algebra into the algebra of n × n matrices and give an explicit representation of such a mapping when n = 2.