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Decomposable multipliers and applications to harmonic analysis

Kjeld Laursen, Michael Neumann (1992)

Studia Mathematica

For a multiplier on a semisimple commutative Banach algebra, the decomposability in the sense of Foiaş will be related to certain continuity properties and growth conditions of its Gelfand transform on the spectrum of the multiplier algebra. If the multiplier algebra is regular, then all multipliers will be seen to be decomposable. In general, an important tool will be the hull-kernel topology on the spectrum of the typically nonregular multiplier algebra. Our investigation involves various closed...

Distinctness of spaces of Lorentz-Zygmund multipliers

Kathryn E. Hare, Parasar Mohanty (2005)

Studia Mathematica

We study the spaces of Lorentz-Zygmund multipliers on compact abelian groups and show that many of these spaces are distinct. This generalizes earlier work on the non-equality of spaces of Lorentz multipliers.

Dual spaces and translation invariant means on group von Neumann algebras

Michael Yin-Hei Cheng (2014)

Studia Mathematica

Let G be a locally compact group. Its dual space, G*, is the set of all extreme points of the set of normalized continuous positive definite functions of G. In the early 1970s, Granirer and Rudin proved independently that if G is amenable as discrete, then G is discrete if and only if all the translation invariant means on L ∞ ( G ) are topologically invariant. In this paper, we define and study G*-translation operators on VN(G) via G* and investigate the problem of the existence of G*-translation invariant...

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