On positive embeddings of CK spacesReport as inadecuate



 On positive embeddings of CK spaces


On positive embeddings of CK spaces - Download this document for free, or read online. Document in PDF available to download.

Download or read this book online for free in PDF: On positive embeddings of CK spaces
We investigate isomorphic embeddings $T: CK\to CL$ 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 $CK$ can be positively embedded into $CL$ then some topological properties of $L$, such as countable tightness of Frechetness, pass to the space $K$. We show that some arbitrary isomorphic embeddings $CK\to CL$ can be, in a sense, reduced to positive embeddings.



Author: Grzegorz Plebanek

Source: https://archive.org/



DOWNLOAD PDF




Related documents