A non-nice extreme operator

1977 ◽  
Vol 26 (3-4) ◽  
pp. 306-312 ◽  
Author(s):  
M. Sharir
Keyword(s):  
Extreme Operator

scholarly journals Extreme operator-valued continuous maps

1991 ◽  
Vol 29 (1-2) ◽  
pp. 73-81 ◽  
Author(s):  
R. Grz⇓ślewicz
Keyword(s):  
Extreme Operator ◽  
Continuous Maps

STRUCTURE TOPOLOGY AND EXTREME OPERATORS

2016 ◽  
Vol 95 (2) ◽  
pp. 315-321
Author(s):  
ANA M. CABRERA-SERRANO ◽  
JUAN F. MENA-JURADO
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Extreme Points ◽  
Closed Unit Ball ◽  
Structure Topology ◽  
Extreme Operator ◽  
Nice Operator

We say that a Banach space $X$ is ‘nice’ if every extreme operator from any Banach space into $X$ is a nice operator (that is, its adjoint preserves extreme points). We prove that if $X$ is a nice almost $CL$-space, then $X$ is isometrically isomorphic to $c_{0}(I)$ for some set $I$. We also show that if $X$ is a nice Banach space whose closed unit ball has the Krein–Milman property, then $X$ is $l_{\infty }^{n}$ for some $n\in \mathbb{N}$. The proof of our results relies on the structure topology.

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