J. Aust. Math. Soc.  81 (2006), 253-278
Homomorphisms of the algebra of locally integrable functions on the half line

 Sandy Grabiner   Department of Mathematics   Pomona College   610 North College Avenue   Claremont, CA 91711   USA  sgrabiner@pomona.edu

Abstract
Let be a continuous nonzero homomorphism of the convolution algebra and also the unique extension of this homomorphism to . We show that the map is continuous in the weak* and strong operator topologies on , considered as the dual space of and as the multiplier algebra of . Analogous results are proved for homomorphisms from to . For each convolution algebra , restricts to a continuous homomorphism from some to some , and, for each sufficiently large , restricts to a continuous homomorphism from some to . We also determine which continuous homomorphisms between weighted convolution algebras extend to homomorphisms of . We also prove results on convergent nets, continuous semigroups, and bounded sets in that we need in our study of homomorphisms.
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