Extreme contractions on continuous vector-valued function spaces

Authors:
Hasan Al-Halees and Richard J. Fleming

Journal:
Proc. Amer. Math. Soc. **134** (2006), 2661-2666

MSC (2000):
Primary 47B38, 46E40

Published electronically:
March 23, 2006

MathSciNet review:
2213745

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Abstract | References | Similar Articles | Additional Information

Abstract: An old question asks whether extreme contractions on are necessarily *nice*; that is, whether the conjugate of such an operator maps extreme points of the dual ball to extreme points. Partial results have been obtained. Determining which operators are extreme seems to be a difficult task, even in the scalar case. Here we consider the case of extreme contractions on , where itself is a Banach space. We show that every extreme contraction on to itself which maps extreme points to elements of norm one is nice, where is compact and is the sequence space .

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Additional Information

**Hasan Al-Halees**

Affiliation:
Department of Mathematics, Saginaw Valley State University, University Center, Michigan 48710-0001

**Richard J. Fleming**

Affiliation:
Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08282-7

Received by editor(s):
March 15, 2005

Received by editor(s) in revised form:
April 1, 2005

Published electronically:
March 23, 2006

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2006
American Mathematical Society