Tensor products of commutative Banach algebras.
The Algebraic Radical of a Normed Ideal in L1 (G).
The convolution-induced topology on (G) and linearly dependent translates in G).
The GRS-condition and symmetry of weighted L¹-algebras
The primitivity of semigroup algebras of free products.
The problem of -simple spectrum for ergodic group automorphisms
The Projection Theorem for Spectral Sets.
The translation invariant uniform approximation property for compact groups
The uniform bounded approximation property with respect to the Haar basis
The Wiener Property for a Class of Discrete Hypergroups.
Über den Satz von Wiener und Lokalkompakte Gruppen
Über ein Problem von Reiter und ein Problem von Derighetti zur Eigenschaft P... lokalkompakter Gruppen
Umbral calculus and cancellative semigroup algebras.
Une preuve rapide du théorème de Beurling et Helson sur les endomorphismes de l'algèbre l¹(Z)
Uniformly continuous functionals on Banach algebras
Uniqueness of rotation invariant norms.
Uniqueness of the topology on L¹(G)
Let G be a locally compact abelian group and let X be a translation invariant linear subspace of L¹(G). If G is noncompact, then there is at most one Banach space topology on X that makes translations on X continuous. In fact, the Banach space topology on X is determined just by a single nontrivial translation in the case where the dual group Ĝ is connected. For G compact we show that the problem of determining a Banach space topology on X by considering translation operators on X is closely related...
Unitary Banach algebras
In a Banach algebra an invertible element which has norm one and whose inverse has norm one is called unitary. The algebra is unitary if the closed convex hull of the unitary elements is the closed unit ball. The main examples are the C*-algebras and the ℓ₁ group algebra of a group. In this paper, different characterizations of unitary algebras are obtained in terms of numerical ranges, dentability and holomorphy. In the process some new characterizations of C*-algebras are given.
Weak amenability of the second dual of a Banach algebra
It is known that a Banach algebra inherits amenability from its second Banach dual **. No example is yet known whether this fails if one considers the weak amenability instead, but the property is known to hold for the group algebra L¹(G), the Fourier algebra A(G) when G is amenable, the Banach algebras which are left ideals in **, the dual Banach algebras, and the Banach algebras which are Arens regular and have every derivation from into * weakly compact. In this paper, we extend this class of...
Weak amenability of weighted group algebras on some discrete groups
Weak amenability of ℓ¹(G,ω) for commutative groups G was completely characterized by N. Gronbaek in 1989. In this paper, we study weak amenability of ℓ¹(G,ω) for two important non-commutative locally compact groups G: the free group ₂, which is non-amenable, and the amenable (ax + b)-group. We show that the condition that characterizes weak amenability of ℓ¹(G,ω) for commutative groups G remains necessary for the non-commutative case, but it is sufficient neither for ℓ¹(₂,ω) nor for ℓ¹((ax + b),ω)...