This is an announcement for the paper "On positive embeddings of C(K) spaces" by Grzegorz Plebanek.

Abstract: We investigate isomorphic embeddings $T: C(K)\to C(L)$ 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 $\pi$-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 $C(K)\to C(L)$ can be, in a sense, reduced to positive embeddings.

Archive classification: math.FA

Submitted from: grzes@math.uni.wroc.pl

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1302.4360

or

http://arXiv.org/abs/1302.4360