Algebras of functions on mappings.
Algebras of holomorphic functions with Hadamard multiplication
A systematic investigation of algebras of holomorphic functions endowed with the Hadamard product is given. For example we show that the set of all non-invertible elements is dense and that each multiplicative functional is continuous, answering some questions in the literature.
Algebras of quotients with bounded evaluation of a normed semiprime algebra
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...
Algebras of real analytic functions; homorphisms and bounding sets.
In this paper weare interested in subsets of a real Banach space on which different classes of functions are bounded.
Algebras whose groups of units are Lie groups
Let A be a locally convex, unital topological algebra whose group of units is open and such that inversion is continuous. Then inversion is analytic, and thus is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then has a locally diffeomorphic exponential function and multiplication is given locally by the Baker-Campbell-Hausdorff series. In contrast, for suitable non-Mackey complete A, the unit group is an analytic Lie group without...
Algebres à bases bornées.
Algebres A-convexes a poids.
Algèbres de Banach ultramétrique et algèbres de Krasner-Tate
Algèbres de Krasner-Tate et générateurs universels
All nuclear C*-algebras are amenable.
Almost commutative -seminormed -algebras. (-algèbres -semi-normées presque commutatives.)
Alternative noetherian Banach algebras.
Sinclair and Tullo [6] proved that noetherian Banach algebras are finite-dimensional. In [3], Grabiner studied noetherian Banach modules. In this paper, we are concerned with alternative noetherian Banach algebras. Combining techniques from [3] with techniques and the result from [6], we prove that every alternative noetherian Banach algebra is finite-dimensional.
Amenability and the second dual of a Banach algebra
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.
Amenability and weak amenability of l¹-algebras of polynomial hypergroups
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.
Amenability for discrete convolution semigroup algebras.
Amenability for dual Banach algebras
We define a Banach algebra 𝔄 to be dual if 𝔄 = (𝔄⁎)* for a closed submodule 𝔄⁎ of 𝔄*. The class of dual Banach algebras includes all W*-algebras, but also all algebras M(G) for locally compact groups G, all algebras ℒ(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certain conditions an amenable...
Amenability in Group Algebras and Banach Algebras.
Amenability of Banach and C*-algebras on locally compact groups
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.
Amenability of Convolution Algebras.
Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey
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, 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 and M(G). For us, “amenability properties” refers to amenability, weak amenability, and biflatness, as well as some properties which...