This is an announcement for the paper "Constructing non-compact operators into $c_0$" by Iryna Banakh and Taras Banakh.

Abstract: We prove that for each dense non-compact linear operator $S:X\to Y$ between Banach spaces there is a linear operator $T:Y\to c_0$ such that the operator $TS:X\to c_0$ is not compact. This generalizes the Josefson-Nissenzweig Theorem.

Archive classification: math.FA

Mathematics Subject Classification: 47B07, 46B15

Remarks: 2 pages

Submitted from: tbanakh@yahoo.com

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

http://front.math.ucdavis.edu/1006.3089

or

http://arXiv.org/abs/1006.3089