I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1997, VOLUME 3, NUMBER 1, PAGES 37-45
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between Banach spaces and is said to be
polynomially continuous (-continuous, for short) if
its restriction to any bounded set is uniformly continuous for the
weak polynomial topology, i.e., for every and bounded
, there are a finite set of
polynomials on and so that
whenever satisfy .
Every compact (linear) operator is -continuous.
The spaces ,
example, admit polynomials which are not -continuous.
We prove that every -continuous operator is
weakly compact and that for every
there is a
scalar valued polynomial on which is not -continuous.
We also characterize the spaces for which uniform continuity and
coincide, as those spaces admitting a separating polynomial.
Other properties of -continuous polynomials
All articles are
published in Russian.
Last modified: November 16, 1999