[Author]
Oleg Reinov
[Title]
Approximation of $p$-summing operators by adjoints
[AMS Subj-class]
47B10 Operators belonging to operator ideals
47A58 Operator approximation theory
[Abstract]
We consider the following question for the ideals $\Pi_p$ of absolutely
$p$-summing operators: Is it true that, for given Banach spaces $X$ and $Y$,
the unit ball of the space $\Pi_p(X,Y)$ is dense, for some natural topology,
in the unit ball of the space $\Pi_p(X,Y^{**})$ or in the unit ball of the
corresponding space
$\Pi_p^{dual}(Y^*,X^*):= \{U: Y^*\to X^*\, |\ U^*|_X\in \Pi_p(X,Y^{**})\}$?
As "natural topologies", we consider strong and weak operator topologies,
compact--open topology, topology of $X\times Y^*$-convergence etc.
[Comments]
LaTeX, English, 8 pp.
[Contact e-mail]
orein51@mail.ru