Abstract:
We study the weak convergence of a greedy algorithm of approximation by a given set
in a Banach space.
It is proved that
the greedy algorithm of approximation by a strongly norm-reducing set
in a uniformly smooth Banach space with the WN-property weakly converges.
In an arbitrary separable Banach space without the WN-property,
we construct an example of a strongly norm-reducing set such that
the greedy algorithm of approximation by this set
does not weakly converge for some initial element.
Bibliography: 6 titles.