Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C∗-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C∗-subalgebra of M(G)∗ = C0(G) ∗∗. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly com...

1. Introduction Let B be a commutative Banach algebra, and let 6 be a homomorphism from B into a Banach algebra A. In this paper we are concerned with establishing conditions on A and B which ensure that 6 is continuous. If A is semisimple, it is well known that any such homomorphism must be continuous, and therefore we shall be interested in cases where A is not semisimple. Questions of this n...

When A is a subalgebra of the commutative Banach algebra C0(X) of all continuous complex-valued functions on a locally compact Hausdorff space X, the spatial numerical range of element of A can be described in terms of positive measures.

Let B be a unital commutative semi-simple Banach algebra. We study endomorphisms of B which are simultaneously Riesz operators. Clearly compact and power compact endomorphisms are Riesz. Several general theorems about Riesz endomorphisms are proved, and these results are then applied to the question of when Riesz endomorphisms of certain algebras are necessarily power compact.

Let R be a commutative complex unital semisimple Banach algebra with the involution ·⋆. Sufficient conditions are given for the existence of a stabilizing solution to the H ∞ Riccati equation when the matricial data has entries from R. Applications to spatially distributed systems are discussed.

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...

Let R be a Banach ring. We prove that the category of chain complexes complete bornological R-modules (and several related categories) is derived algebraic context in sense Raksit. then use framework algebra to version Hochschild-Kostant-Rosenberg Theorem, which relates circle action on Hochschild de Rham-differential-enriched-de Rham simplicial, commutative, algebra. This has geometric interpr...

We consider Akbarov's holomorphic version of the non-commutative Pontryagin duality for a complex Lie group. prove, under assumption that $G$ is Stein group with finitely many components, (1) topological Hopf algebra functions on holomorphically reflexive if and only linear; (2) dual cocommutative exponential analytic functional reflexive. give counterexample, which shows first criterion cannot...