Abstract

Let X be a completely regular Hausdorff space and E be a Banach space. Let C_b(X, E) (resp. ) be the space of all bounded continuous (resp. bounded strongly Borel-measurable) functions f : X → E, equipped with the natural mixed topologies. Then whenever X or E is separable. We study the problem of extension of different classes of continuous linear operators acting from C_b(X, E) to a Banach space F to corresponding continuous linear operators acting from to F.

中文翻译：

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Cb(X, E) 上连续线性算子的扩展

摘要

令X为完全正则 Hausdorff 空间，E为 Banach 空间。令C _b ( X , E ) (resp. ) 为所有有界连续（即有界强 Borel 可测）函数f : X → E的空间，配备自然混合拓扑。然后只要X或E是可分离的。我们研究了从C _b ( X, E ) 到 Banach 空间F的不同类别的连续线性算子扩展到对应的连续线性算子的问题到F。