On onesided harmonic analysis in non commutative locally compact groups.
On Primary Ideals in the Group Algebra of a Nilpotent Lie Group.
On some spaces of linear functionals on the algebras for locally compact groups
On the dual of a Commutative signed Hypergroup.
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)) contains a linear isometric copy of when G is a normal non-P-group. When G is not a P-group but not necessarily normal we prove that the quotient is non-separable. For non-discrete P-groups, the quotient may sometimes be trivial and sometimes non-separable. When G is locally compact, we show that the quotient space LUC(G)/WAP(G) contains a linear isometric copy of , where κ(G) is the minimal number of compact sets needed to cover G. This leads to the extreme non-Arens regularity of the group algebra L¹(G) when in addition either κ(G) is greater than or equal to the smallest cardinality of an open base at the identity e of G, or G is metrizable. These results are improvements and generalizations of theorems proved by various authors along the last 35 years and until very recently.
On the Spectrum of Convolution Operators on Groups with Polynomial Growth.
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...
On Weyl's reciprocity between group algebras and their commutants
Operators of Finite Rank in Unitary Representations of Exponential Lie Groups.
Polynomidentitäten und Permutationsdarstellungen lokalkompakter Gruppen.
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...
Radial functions on free groups and a decomposition of the regular representation into irreducible components.
Räume primitiver Ideale von Gruppenalgebren.
Recapturing semigroup compactifications of a group from those of its closed normal subgroups.
Reciprocity theorems in the theory of representations of groups and algebras [Book]
*-Regularity of Exponential Lie Groups.
Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness
Let G be a locally compact amenable group, and A(G) and B(G) the Fourier and Fourier-Stieltjes algebras of G. For a closed subset E of G, let J(E) and k(E) be the smallest and largest closed ideals of A(G) with hull E, respectively. We study sets E for which the ideals J(E) or/and k(E) are σ(A(G),C*(G))-closed in A(G). Moreover, we present, in terms of the uniform topology of C₀(G) and the weak* topology of B(G), a series of characterizations of sets obeying synthesis. Finally, closely related to...
Remarks on Segal Algebras.
Representations of Double Coset Hypergroups and Induced Representations.