An extension of Elton's theorem to complex Banach spaces

Authors:
S. J. Dilworth and Joseph P. Patterson

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1489-1500

MSC (2000):
Primary 46B07; Secondary 46B04, 46B09

DOI:
https://doi.org/10.1090/S0002-9939-02-06651-0

Published electronically:
September 5, 2002

MathSciNet review:
1949879

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be sufficiently small. Then, for , there exists such that if are vectors in the unit ball of a complex Banach space which satisfy

(where are independent complex Steinhaus random variables), then there exists a set , with , such that

for all (). The dependence on of the threshold proportion is sharp.

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Additional Information

**S. J. Dilworth**

Affiliation:
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208

Address at time of publication:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

Email:
dilworth@math.sc.edu

**Joseph P. Patterson**

Affiliation:
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208

Address at time of publication:
2110 Arrowcreek Dr., Apt. 101, Charlotte, North Carolina 28273

Email:
joe_p_chess@yahoo.com

DOI:
https://doi.org/10.1090/S0002-9939-02-06651-0

Received by editor(s):
October 17, 2001

Received by editor(s) in revised form:
December 11, 2001

Published electronically:
September 5, 2002

Additional Notes:
The research of the first author was completed while on sabbatical as a Visiting Scholar at The University of Texas at Austin.

This paper is based on the second author’s thesis for his MS degree at the University of South Carolina.

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2002
American Mathematical Society