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.
On the Property P... of Locally Compact Groups
On the Silov boundary induced by certain semigroup algebras
On the size of quotients of function spaces on a topological group
For a non-precompact topological group G, we consider the space C(G) of bounded, continuous, scalar-valued functions on G with the supremum norm, together with the subspace LMC(G) of left multiplicatively continuous functions, the subspace LUC(G) of left norm continuous functions, and the subspace WAP(G) of weakly almost periodic functions. We establish that the quotient space LUC(G)/WAP(G) contains a linear isometric copy of , and that the quotient space C(G)/LMC(G) (and a fortiori C(G)/LUC(G))...
On the spectral radius in
On the Spectrum of Convolution Operators on Groups with Polynomial Growth.
On the spectrum of the Laplacian on the affine group of the real line
On the Symmetry of Generalized L1-Algebras.
On the uniqueness of uniform norms and C*-norms
We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm; this is...
Power boundedness in Banach algebras associated with locally compact groups
Let G be a locally compact group and B(G) the Fourier-Stieltjes algebra of G. Pursuing our investigations of power bounded elements in B(G), we study the extension property for power bounded elements and discuss the structure of closed sets in the coset ring of G which appear as 1-sets of power bounded elements. We also show that L¹-algebras of noncompact motion groups and of noncompact IN-groups with polynomial growth do not share the so-called power boundedness property. Finally, we give a characterization...
Primary Ideal in Centers of Group Algebras.
Problèmes de l'unicité, de la synthèse et des isomorphismes en analyse harmonique
Projections in C*-Algebras of nilpotent groups.
Pseudo-amenability of Brandt semigroup algebras
In this paper it is shown that for a Brandt semigroup over a group with an arbitrary index set , if is amenable, then the Banach semigroup algebra is pseudo-amenable.
Remarks on Segal Algebras.
Representation theory of locally -convex topological algebras