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Zeitschrift für Analysis und ihre Anwendungen


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Volume 10, Issue 4, 1991, pp. 433–438
DOI: 10.4171/ZAA/465

Published online: 1991-12-31

Exposed Operators in $\mathcal B (C(X), C(Y))$

Ryszard Grząślewicz

A point $q_0$ in a convex set $Q$ is exposed if there exists a bounded linear functional $\xi$ such that $\xi(q_0)$ for all $q \in Q\ \{q_0\}$. Characterizations of exposed points of the unit ball and the positive part of the unit ball of $\mathcal B (C(X), C(Y))$ are given. We describe the set of strongly exposed points. We also consider exposed operators on $L^\{infty}$- and $L^1$-spaces.

Keywords: Exposed points, space of continuous functions, operators, Nice operators, strongly exposed operators

Grząślewicz Ryszard: Exposed Operators in $\mathcal B (C(X), C(Y))$. Z. Anal. Anwend. 10 (1991), 433-438. doi: 10.4171/ZAA/465