Weighted convolution algebras on subsemigroups of the real line

H. G. Dales, and H. V. Dedania. Weighted convolution algebras on subsemigroups of the real line. 2009. <http://eudml.org/doc/285976>.

@book{H2009,
abstract = {In this memoir, we shall consider weighted convolution algebras on discrete groups and semigroups, concentrating on the group (ℚ,+) of rational numbers, the semigroup $(ℚ^\{+•\},+)$ of strictly positive rational numbers, and analogous semigroups in the real line ℝ. In particular, we shall discuss when these algebras are Arens regular, when they are strongly Arens irregular, and when they are neither, giving a variety of examples. We introduce the notion of ’weakly diagonally bounded’ weights, weakening the known concept of ’diagonally bounded’ weights, and thus obtaining more examples. We shall also construct an example of a weighted convolution algebra on ℕ that is neither Arens regular nor strongly Arens irregular, and an example of a weight ω on $ℚ^\{+•\}$ such that $lim inf_\{s→ 0+\}ω(s) =0$.},
author = {H. G. Dales, H. V. Dedania},
keywords = {Arens products; Arens regularity; topological centre; weight; Beurling algebra; weighted convolution algebra; strong Arens irregularity},
language = {eng},
title = {Weighted convolution algebras on subsemigroups of the real line},
url = {http://eudml.org/doc/285976},
year = {2009},
}

TY - BOOK
AU - H. G. Dales
AU - H. V. Dedania
TI - Weighted convolution algebras on subsemigroups of the real line
PY - 2009
AB - In this memoir, we shall consider weighted convolution algebras on discrete groups and semigroups, concentrating on the group (ℚ,+) of rational numbers, the semigroup $(ℚ^{+•},+)$ of strictly positive rational numbers, and analogous semigroups in the real line ℝ. In particular, we shall discuss when these algebras are Arens regular, when they are strongly Arens irregular, and when they are neither, giving a variety of examples. We introduce the notion of ’weakly diagonally bounded’ weights, weakening the known concept of ’diagonally bounded’ weights, and thus obtaining more examples. We shall also construct an example of a weighted convolution algebra on ℕ that is neither Arens regular nor strongly Arens irregular, and an example of a weight ω on $ℚ^{+•}$ such that $lim inf_{s→ 0+}ω(s) =0$.
LA - eng
KW - Arens products; Arens regularity; topological centre; weight; Beurling algebra; weighted convolution algebra; strong Arens irregularity
UR - http://eudml.org/doc/285976
ER -