This is an announcement for the paper "On operator relations between locally convex spaces" by Ersin Kizgut, Elif Uyanik, and Murat Yurdakul.
Abstract: A linear operator $T:X \to Y$ between vector spaces is called strictly singular if for any infinite dimensional closed vector subspace $M$ of $X$, the restriction of $T$ on $M$ is not a topological isomorphism. In this note we introduced some sufficient conditions on domain and range spaces such that any bounded linear operator in between is strictly singular, and give some examples of spaces satisfying these conditions.
Archive classification: math.FA
Remarks: 15 pages, presented in the context of 8th Australian and New
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.5761
or