On positive embeddings of C(K) spaces

2013/02/18 by Plebanek, Grzegorz
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1302.4360

Abstract

We investigate isomorphic embeddings T: C(K)→ C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is an image of L under a upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets which closures a continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such as countable tightness of Frechetness, pass to the space K. We show that some arbitrary isomorphic embeddings C(K)→ C(L) can be, in a sense, reduced to positive embeddings.

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