Local existence of -sets, projective tensor products, and Arens regularity for

Author:
Colin C. Graham

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1963-1971

MSC (2000):
Primary 43A15, 43A10; Secondary 46L10

DOI:
https://doi.org/10.1090/S0002-9939-04-07159-X

Published electronically:
February 6, 2004

MathSciNet review:
2053967

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Abstract | References | Similar Articles | Additional Information

Abstract: **Theorem.** *If are perfect compact subsets of the locally compact metrizable abelian group, then there are pairwise disjoint perfect subsets such that* (i) *is either a Kronecker set or* (ii) *for some , is a translate of a -set all of whose elements have order , and* (iii) *is isomorphic to the projective tensor product .*

This extends what was previously known for groups such as or for the case to the general locally compact abelian group. Old results concerning the local existence of Kronecker and -sets are improved.

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Additional Information

**Colin C. Graham**

Affiliation:
Department of Mathematics, University of British Columbia, RR#1–H-46, Bowen Island, British Columbia, Canada V0N 1G0

Email:
ccgraham@alum.mit.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07159-X

Keywords:
Arens regularity,
bidual,
Kronecker set,
$K_{p}$-set,
locally compact abelian groups,
projective tensor product,
quotients of the Fourier algebra,
set sums,
tensor algebra

Received by editor(s):
September 12, 2002

Received by editor(s) in revised form:
December 23, 2002

Published electronically:
February 6, 2004

Additional Notes:
Preprints of a draft of this paper were circulated under the title “Arens regularity and related matters for $A(E+F)$”.

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2004
American Mathematical Society