A note on a theorem of Tacon
by
Sergio Falcon
University of Las Palmas de Gran Canaria
Coauthors: K. Sadarangani

In this paper we give the minimal conditions in a certain sense for the proofs of a theorem of Tacon and analogous results for some other classes of operators can be reproduced.

We prove that if M is a family of bounded, countable sets of a Banach space F, defining a structure of operators on F which is sequentially determined, then for a Banach space E and a sequence of operators (T_n) subset L(E, F), the following assertions are equivalent:
a) There exists n₀ in N such that T_n0 is an M-operator
b) For every bounded sequence (x_n) in E, there exists p in N such that {T_px_n: n in N} in M

Date received: March 8, 2001