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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Contractive projections on $ C\sb{0}(K)$


Authors: Yaakov Friedman and Bernard Russo
Journal: Trans. Amer. Math. Soc. 273 (1982), 57-73
MSC: Primary 46L05; Secondary 17C65, 46J05
MathSciNet review: 664029
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Abstract: We show that the range of a norm one projection on a commutative $ {C^\ast}$-algebra has a ternary product structure (Theorem 2). We describe and characterize all such projections in terms of extreme points in the unit ball of the image of the dual (Theorem 1). We give necessary and sufficient conditions for the range to be isometric to a $ {C^\ast}$-algebra (Theorem 4) and we show that the range is a $ {C_\sigma }$-space (Theorem 5).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0664029-4
PII: S 0002-9947(1982)0664029-4
Keywords: Norm one projection, ternary algebra, Jordan triple system, $ {C^\ast}$-algebra, averaging operator, $ {C_\sigma }$-space
Article copyright: © Copyright 1982 American Mathematical Society