A set of linear operators from
one topological vector space to another is said to be collectively compact (resp.
semi-compact) if and only if the union of images of a neighbourhood of zero
(respectively every bounded set) is relatively compact. In this paper sufficient
conditions for a set of operators to be collectively compact or semi-compact are
obtained. It is proved that if Tn→ T asymptotically, where X is quasi-complete and
Tn are W-compact then {Tn− T} is collectively compact. The final section deals
with collectively weakly compact sets. It is proved that in a reflexive locally convex
space a family of continuous endomorphisms is collectively weakly compact if and
only if
