Extreme operators in the unit ball of over the complex field

Author:
Alan Gendler

Journal:
Proc. Amer. Math. Soc. **57** (1976), 85-88

MSC:
Primary 47D20

MathSciNet review:
0405173

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Abstract: Assume that and are compact Hausdorff spaces and that and are the Banach spaces of continuous complex-valued functions on and , respectively. is the space of bounded linear operators from to . If is a Banach space, then is the closed unit ball in . An operator in is *nice* if . For each denotes point mass at . The main theorem states that if is extreme in and for all , then is nice. Other theorems are proved by using the same techniques as in the proof of the main theorem.

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DOI:
https://doi.org/10.1090/S0002-9939-1976-0405173-9

Keywords:
Extreme operators,
nice operators,
compact operator,
extremally disconnected,
basically disconnected

Article copyright:
© Copyright 1976
American Mathematical Society