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Let X be a completely regular Hausdorff space, and let C  b (X) denote the Banach space of all real-valued bounded continuous functions on X. We study linear operators from C  b (X) provided with the strict topology β  σ  to a Banach space $${(E,\|\cdot\|_E)}$$. In particular, we derive a Yosida–Hewitt type decomposition for weakly compact operators from C  b (X) to E.

Linear operators on the space of bounded continuous functions with strict topologies