[Author]
 Oleg Reinov

[Title]
 Approximation of operators in dual spaces by adjoints

[AMS Subj-class]
 46B28 Spaces of operators; tensor products; approximation properties

[Abstract]
   Let X,Y be Banach spaces, T: Y^*\to X^* be a linear continuous operator.
 Is it possible to approximate T by operators of kind S^*: Y^*\to X^* 
 (adjoint to the operators from X to Y) in the topologies of compact
 convergence in L(Y^*,X^*) and pointwise X\times Y^*-convergence in L(Y^*,X^*),
 as well as to approximate the operator T^*|_X: X\to Y^{**} in corresponding 
 topologies by operators acting from X to Y?
   The properties of (C,k)-metric approximation are intriduced. Some sufficient
 (and, in a sence, necessary) conditions are given for the approximation of T
 (or T^*|_X) on all k-dimensional subspaces of corresponding spaces.
 Some examples are considered of the operators which can not be approximated
 (e.g., X\times Y^*-pointwise), - for Banach spaces with AP, but without MAP,
 for the spaces with AP and MAP, for the spaces without AP.

[Comments]
 LaTeX, Russian, 10 pp.

[Contact e-mail]
 orein51@mail.ru