Complex analytic properties of certain uniform Fréchet-Schwartz algebras
Complex borel structure in JC-algebras.
Compressible operators and the continuity of homomorphisms from algebras of operators
The notion of a compressible operator on a Banach space, E, derives from automatic continuity arguments. It is related to the notion of a cartesian Banach space. The compressible operators on E form an ideal in ℬ(E) and the automatic continuity proofs depend on showing that this ideal is large. In particular, it is shown that each weakly compact operator on the James' space, J, is compressible, whence it follows that all homomorphisms from ℬ(J) are continuous.
Computing and estimating the global dimension in certain classes af Banach algebras.
Concerning a problem of Arens on removable ideals in Banach algebras
Concerning entire functions in -algebras
We construct a non-m-convex non-commutative -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.
Concerning spectral characterizations of the radical in Banach algebras
Concerning topologization of real or complex algebras
Connes amenability-like properties
We introduce and study the notions of w*-approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We prove that the dual Banach sequence algebra ℓ¹ is not w*-approximately Connes amenable. We show that in general the concepts of pseudo-Connes amenability and Connes amenability are distinct. Moreover the relations between these new notions are also discussed.
Constructions preserving -weak amenability of Banach algebras
A surjective bounded homomorphism fails to preserve -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.
Continuité automatique des dérivations et des epimorphismes II.
Continuité des caractères des algèbres localement multiplicativement convexes
Continuité des homomorphismes d'une algèbre métrisable et complète sur certaines algèbres de Banach.
Continuité et uniforme continuité du spectre dans les algèbras de Banach
Continuity of a homomorphism on commutative subalgebras is not sufficient for continuity
Continuity of characters in products of algebras
Continuity of derivations from radical convolution algebras
Continuity of derivations on a complete normed alternative algebra
Continuity of derivations on semi-prime Banach algebras.
Continuity of generalized inverses in Banach algebras
The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.