[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