Multipliers of certain convolution algebras over locally compact semigroups

1980 ◽  
Vol 87 (1) ◽  
pp. 51-59 ◽  
Author(s):  
D. G. Todd
Keyword(s):  
Ordered Semigroup ◽  
Real Numbers ◽  
Locally Compact ◽  
Multiplier Algebra ◽  
Similar Work ◽  
Convolution Algebras ◽  
Compact Semigroups ◽  
Integrable Functions ◽  
Locally Compact Semigroups

In this paper we extend a result of Johnson and Lahr(3), which characterizes the multiplier algebra of L1(a, b) (the algebra of Lebesgue integrable functions on the interval of real numbers from a to b, under order convolution) to the L1 algebra of a general totally ordered semigroup. Similar work has been done in (l), but under more restrictive conditions.

On the Semigroup of Probability Measures of a Locally Compact Semigroup II

1987 ◽  
Vol 30 (3) ◽  
pp. 273-281 ◽  
Author(s):  
James C. S. Wong
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Fixed Point Properties ◽  
The Relationship ◽  
Locally Compact Semigroups

AbstractThis is a sequel to the author's paper "On the semigroup of probability measures of a locally compact semigroup." We continue to investigate the relationship between amenability of spaces of functions and functionals associated with a locally compact semigroups S and its convolution semigroup MO(S) of probability measures and fixed point properties of actions of S and MO(S) on compact convex sets.

Measure in Semigroups

1952 ◽  
Vol 4 ◽  
pp. 396-406 ◽  
Author(s):  
B. R. Gelbaum ◽  
G. K. Kalisch
Keyword(s):  
Topological Group ◽  
Invariant Measure ◽  
Commutative Semigroup ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Counter Example ◽  
Compact Semigroups ◽  
Topological Measures ◽  
Weakened Form ◽  
Locally Compact Semigroups

The major portion of this paper is devoted to an investigation of the conditions which imply that a semigroup (no identity or commutativity assumed) with a bounded invariant measure is a group. We find in §3 that a weakened form of “shearing” is sufficient and a counter-example (§5) shows that “shearing” may not be dispensed with entirely. In §4 we discuss topological measures in locally compact semigroups and find that shearing may be dropped without affecting the results of the earlier sections (Theorem 2). The next two theorems show that under certain circumstances (shearing or commutativity) the topology of the semigroup (already known to be a group by virtue of earlier results) can be weakened so that the structure becomes a separated compact topological group. The last section treats the problem of extending an invariant measure on a commutative semigroup to an invariant measure on its quotient structure.

scholarly journals Homomorphisms of the algebra of locally integrable functions on the half line

2006 ◽  
Vol 81 (2) ◽  
pp. 253-278 ◽  
Author(s):  
Sandy Grabiner
Keyword(s):  
Dual Space ◽  
Continuous Homomorphism ◽  
Half Line ◽  
Unique Extension ◽  
Multiplier Algebra ◽  
Convolution Algebra ◽  
Convolution Algebras ◽  
Integrable Functions ◽  
Bounded Sets ◽  
Nonzero Homomorphism

AbstractLet φ be a continuous nonzero homomorphism of the convolution algebra L1loc(R+) and also the unique extension of this homomorphism to Mloc(R+). We show that the map φis continuous in the weak* and strong opertor topologies on Mloc, considered as the dual space of Cc(R+) and as the multiplier algebra of L1loc. Analogous results are proved for homomorphism from L1 [0, a) to L1 [0, b). For each convolution algebra L1 (ω1), φ restricts to a continuous homomorphism from some L1 (ω1) to some L1 (ω2), and, for each sufficiently large L1 (ω2), φ restricts to a continuous homomorphism from some L1 (ω1) to L1 (ω2). We also determine which continuous homomorphisms between weighted convolution algebras extend to homomorphisms of L1loc. We also prove results on convergent nets, continuous semigroups, and bounded sets in Mloc that we need in our study of homomorphisms.

scholarly journals Right invariant integrals on locally compact semigroups

1964 ◽  
Vol 4 (3) ◽  
pp. 273-286 ◽  
Author(s):  
J. H. Michael
Keyword(s):  
Compact Semigroup ◽  
Compact Sets ◽  
Property A ◽  
Locally Compact ◽  
Invariant Integrals ◽  
Positive Linear Functional ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Image Position ◽  
Locally Compact Semigroups

An integral on a locally compact Hausdorff semigroup ς is a non-trivial, positive, linear functional μ on the space of continuous real-valued functions on ς with compact supports. If ς has the property: (A) for each pair of compact sets C, D of S, the set is compact; then, whenever and a ∈ S, the function fa defined by is also in . An integral μ on a locally compact semigroup S with the property (A) is said to be right invariant if for all j ∈ and all a ∈ S.

Compact right multipliers on a Banach algebra related to locally compact semigroups

2011 ◽  
Vol 83 (2) ◽  
pp. 205-213 ◽  
Author(s):  
Saeid Maghsoudi ◽  
Mohammad Javad Mehdipour ◽  
Rasoul Nasr-Isfahani
Keyword(s):  
Banach Algebra ◽  
Locally Compact ◽  
Compact Semigroups ◽  
Locally Compact Semigroups

Quotients of locally compact semigroups

1981 ◽  
Vol 22 (1) ◽  
pp. 277-281
Author(s):  
Bernard L. Madison
Keyword(s):  
Locally Compact ◽  
Compact Semigroups ◽  
Locally Compact Semigroups
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