Some strict inclusions between spaces of -multipliers

Author:
J. F. Price

Journal:
Trans. Amer. Math. Soc. **152** (1970), 321-330

MSC:
Primary 46.35; Secondary 42.00

DOI:
https://doi.org/10.1090/S0002-9947-1970-0282210-5

MathSciNet review:
0282210

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that the Hausdorff topological group is either compact or locally compact abelian and that denotes the set of continuous complex-valued functions on with compact supports. Let denote the restrictions to of the continuous linear operators from into which commute with all the right translation operators.

When or it is known that

When is compact, simple relations will also be developed between idempotent operators in and lacunary subsets of the dual of which will enable us to find necessary conditions so that inclusion (1) is strict even if, for example, and are replaced by the sets of idempotent operators in and respectively.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0282210-5

Keywords:
Lebesgue function spaces,
locally compact abelian groups,
compact groups,
translations,
multiplier operators,
idempotent multiplier operators

Article copyright:
© Copyright 1970
American Mathematical Society