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Algebras whose groups of units are Lie groups

Helge Glöckner (2002)

Studia Mathematica

Let A be a locally convex, unital topological algebra whose group of units A × is open and such that inversion ι : A × → A × is continuous. Then inversion is analytic, and thus A × is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then A × 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 A × is an analytic Lie group without...

Alternative noetherian Banach algebras.

M. Benslimane, N. Boudi (1997)

Extracta Mathematicae

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

Frédéric Gourdeau (1997)

Studia Mathematica

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

Rupert Lasser (2007)

Studia Mathematica

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 dual Banach algebras

V. Runde (2001)

Studia Mathematica

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 of Banach and C*-algebras on locally compact groups

A. Lau, R. Loy, G. Willis (1996)

Studia Mathematica

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 properties of Fourier algebras and Fourier-Stieltjes algebras: a survey

Nico Spronk (2010)

Banach Center Publications

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 ( G ) 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 ( G ) and M(G). For us, “amenability properties” refers to amenability, weak amenability, and biflatness, as well as some properties which...

An additivity formula for the strict global dimension of C(Ω)

Seytek Tabaldyev (2014)

Open Mathematics

Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .

An amalgamation of the Banach spaces associated with James and Schreier, Part II: Banach-algebra structure

Alistair Bird (2010)

Banach Center Publications

The James-Schreier spaces, defined by amalgamating James' quasi-reflexive Banach spaces and Schreier space, can be equipped with a Banach-algebra structure. We answer some questions relating to their cohomology and ideal structure, and investigate the relations between them. In particular we show that the James-Schreier algebras are weakly amenable but not amenable, and relate these algebras to their multiplier algebras and biduals.

Currently displaying 81 – 100 of 151