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Journal of the London Mathematical Society Advance Access originally published online on January 29, 2007
Journal of the London Mathematical Society 2007 75(1):176-186; doi:10.1112/jlms/jdl010
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© 2007 London Mathematical Society

The l{infty} direct sum of Lp (1 < p < {infty}) is primary

H. M. Wark

9 Westwood Terrace
South Bank
York
North Yorkshire YO23 1HJ
United Kingdom
hughwark{at}yahoo.com

Using Szemeredi's theorem on arithmetic progressions, it is shown that, for 1 < p < {infty}, the infinite l{infty} direct sum (Lp {oplus} Lp {oplus} · · · )l{infty} is a primary Banach space.

2000 Mathematics Subject Classification 46B03, 46B25

Received September 7, 2001; revised May 17, 2006; published online January 29, 2007.


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