The predual of the space of convolutors on a locally compact group

Abstract

Let Cv p ( G ) be the space of convolution operators on the Lebesgue space L P ( G ), for an arbitrary locally compact group G . We describe Cv p ( G ) as a dual space, whose predual, is a Banach algebra of functions on G , under pointwise operations, with maximal ideal space G . This involves a variation of Herz's definition of A P ( G ); the benefit of this new definition is that all of Cv p ( G ) is obtained as the dual in the nonamenable setting. We also discuss further developments of this idea.

Locations

• Bulletin of the Australian Mathematical Society - View - PDF