This is an announcement for the paper "Extension and lifting of operators and polynomials" by Jesus M.F. Castillo, Ricardo Garcia, and Jesus Suarez.

Abstract: We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of $\mathcal{L}_1$ and $\mathcal{L}_{\infty}$-spaces that includes and extends those of Lindenstrauss-Rosenthal \cite{LR} using compact operators and Gonz'{a}lez-Guti'{e}rrez \cite{GG} using compact polynomials. We display several examples to show the difference between extending and lifting compact (resp. weakly compact, unconditionally convergent, separable and Rosenthal) operators to operators of the same type. Finally, we show the previous results in a homological perspective, which helps the interested reader to understand the motivations and nature of the results presented.

Archive classification: math.FA

Remarks: to appear in Mediterranean J. of Mathematics

Submitted from: castillo@unex.es

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

http://front.math.ucdavis.edu/1106.5088

or

http://arXiv.org/abs/1106.5088