On a New Segal Algebra.
On Banach algebras satisfying a spectral maximum principle
On Beurling measure algebras
We show how the measure theory of regular compacted-Borel measures defined on the -ring of compacted-Borel subsets of a weighted locally compact group provides a compatible framework for defining the corresponding Beurling measure algebra , thus filling a gap in the literature.
On Bounded Approximate Units in Ideals of Group Algebras*
On character amenable Banach algebras
We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A...
On Cohen's proof of the Factorization Theorem
Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.
On Complete Regularity of Group Algebras.
On derivations and crossed homomorphisms
We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general,...
On Discontinuous Homomorphisms of L1(G).
On Existence of Finite Universal Korovkin Sets in the Centre of Group Algebras.
On generalized Beurling’s theorem and symmetry of -group algebras
On group algebras of nilpotent Lie groups
On left -biflat Banach algebras
We study the notion of left -biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra is left -biflat if and only if is amenable. Also we characterize left -biflatness of semigroup algebra in terms of biflatness, when is a Clifford semigroup.
On Lp Fourier Multipliers on a Compact Lie-Group.
On Maximal Ideals in Group Algebras of SIN-Groups.
On onesided harmonic analysis in non commutative locally compact groups.
On spectrality of the algebra of convolution dominated operators
If G is a discrete group, the algebra CD(G) of convolution dominated operators on l²(G) (see Definition 1 below) is canonically isomorphic to a twisted L¹-algebra . For amenable and rigidly symmetric G we use this to show that any element of this algebra is invertible in the algebra itself if and only if it is invertible as a bounded operator on l²(G), i.e. CD(G) is spectral in the algebra of all bounded operators. For G commutative, this result is known (see [1], [6]), for G noncommutative discrete...
On symmetry of group algebras of discrete nilpotent groups
On the Banach algebra A (...) for smooth sets ... Rn.
On the projectivity and flatness of some group modules
In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.