### A characterization of singular endomorphisms of a barrelled Ptak space.

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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 properly infinite C*-algebra has no non-zero traces. We construct properly infinite Banach *-algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly "close" to the class of C*-algebras, in the sense that they can be hermitian or *-semisimple.

We deal with the algebras consisting of the quotients that produce bounded evaluation on suitable ideals of the multiplication algebra of a normed semiprime algebra A. These algebras of quotients, which contain A, are subalgebras of the bounded algebras of quotients of A, and they have an algebra seminorm for which the relevant inclusions are continuous. We compute these algebras of quotients for some norm ideals on a Hilbert space H: 1) the algebras of quotients with bounded evaluation of the ideal...

Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.

We investigate amenability and weak amenability of the l¹-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, we prove amenability for the hypergroup induced by the Chebyshev polynomials of the first kind.

Several results are given about the amenability of certain algebras defined by locally compact groups. The algebras include the C*-algebras and von Neumann algebras determined by the representation theory of the group, the Fourier algebra A(G), and various subalgebras of these.

Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, ${L}^{-1}\left(G\right)$ and M(G), in a sense which generalizes the Pontryagin duality theorem on abelian groups. We wish to consider the amenability properties of A(G) and B(G) and compare them to such properties for ${L}^{-1}\left(G\right)$ and M(G). For us, “amenability properties” refers to amenability, weak amenability, and biflatness, as well as some properties which...

We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where $A={\ell}^{p}$ for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras ${\ell}^{p}\left(\omega \right)$.