关于C(K)到C(K)的所有正则算子的空间

Indagationes Mathematicae (Proceedings) Pub Date : 1988-09-26 DOI:10.1016/S1385-7258(88)80001-5

A. Andreu, J.M. Mazón, S. Segura de Léon

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引用次数: 1

摘要

已知从E到C(K)的所有正则算子的空间Lr(E, C(K))是所有Riesz空间E的Riesz空间当且仅当K是斯通的。如果用C(K)代替E，证明了这个命题成立，其中K是紧空间，其基数满足一定条件。

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On the space of all regular operators from C(K) into C(K)

It is known that L^r(E, C(K)), the space of all regular operators from E into C(K), is a Riesz space for all Riesz spaces E if and only if K is Stonian. We prove that this statement holds if E is replaced by C(K), where K is a compact space, the cardinal number of which satisfies a certain condition.

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Indagationes Mathematicae (Proceedings)

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