A generalization of the -weak amenability of Banach algebras.
A generalization of the weak amenability of Banach algebras.
A generalized notion of -weak amenability
In the current work, a new notion of -weak amenability of Banach algebras using homomorphisms, namely --weak amenability is introduced. Among many other things, some relations between --weak amenability of a Banach algebra and , the Banach algebra of matrices with entries from , are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra is ()--weakly amenable for any...
A geometric condition equivalent to commutativity in Banach algebras
A glimpse at the theory of Jordan-Banach triple systems.
In this article, a survey of the theory of Jordan-Banach triple systems is presented. Most of the recent relevant results in this area have been included, though no proofs are given.
A Holomorphic Characterization of Jordan C*-Algebras.
A Jacobson-semisimple Banach algebra with a dense nil subalgebra
A Kleinecke-Shirokov type condition with Jordan automorphisms
Let φ be a Jordan automorphism of an algebra . The situation when an element a ∈ satisfies is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma.
A Künneth formula in topological homology and its applications to the simplicial cohomology of
We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex of Banach spaces and continuous boundary maps dₙ with closed ranges and prove that Hⁿ(’) ≅ Hₙ()’, where Hₙ()’ is the dual space of the homology group of and Hⁿ(’) is the cohomology group of the dual complex ’. A Künneth formula for chain complexes of nuclear Fréchet spaces and continuous boundary maps with closed ranges is also obtained. This enables us to describe explicitly...
A local version of the Dauns-Hofmann theorem.
A measure induced metric topology for a Banach algebra
A multi-dimensional spectral theory in C*-algebras
A new order relation for JB-algebras
A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.
We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].
A non-locally convex topological algebra with all commutative subalgebras locally convex
We construct a complete multiplicatively pseudoconvex algebra with the property announced in the title. This solves Problem 25 of [6].
A non-m-convex algebra on which operate all entire functions
A note on a class of Banach algebra-valued polynomials.
A note on a construction of J. F. Feinstein
In [6] J. F. Feinstein constructed a compact plane set X such that R(X), the uniform closure of the algebra of rational functions with poles off X, has no non-zero, bounded point derivations but is not weakly amenable. In the same paper he gave an example of a separable uniform algebra A such that every point in the character space of A is a peak point but A is not weakly amenable. We show that it is possible to modify the construction in order to produce examples which are also regular.
A note on criteria of Le Page and Hirschfeld-Żelazko for the commutativity of Banach algebras
A note on distribution spaces on manifolds.