[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