8 research outputs found
Convex-Cyclic Weighted Translations On Locally Compact Groups
A bounded linear operator on a Banach space is called a convex-cyclic
operator if there exists a vector such that the convex hull of
is dense in . In this paper, for given an aperiodic element
in a locally compact group , we give some sufficient conditions for a
weighted translation operator on
to be convex-cyclic. A necessary condition is also
studied. At the end, to explain the obtained results, some examples are given
On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups
Let be a locally compact group with a fixed left Haar measure and Ω be a system of weights on . In this paper, we deal with locally convex space (,Ω) equipped with the locally convex topology generated by the family of norms (‖.‖,)∈Ω. We study various algebraic and topological properties of the locally convex space (,Ω). In particular, we characterize its dual space and show that it is a semireflexive space. Finally, we give some conditions under which (,Ω) with the convolution multiplication is a topological algebra and then characterize its closed ideals and its spectrum
Porosity of certain subsets of Lebesgue spaces on locally compact groups
Let be a locally compact group. In this paper, we show that if is a non-discrete locally compact group, and , then the set of all pairs for which is finite, forms a set of first category in .
10.1017/S000497271200094
Porosity and the lp-conjecture for semigroups
In this paper, we consider the size of the set ( f, g) ∈ p(S) × q (S) : ∃ x ∈ S, | f |∗|g|(x) 0. By means of this notion of porosity we also provide a strengthening of a famous result by Rajagopalan on the p-conjecture