ON THE CONVERGENCE RATE OF S-NUMBERS OF COMPACT HANKEL-OPERATORS

It is well known that the sequence of s-numbers {sn}, n=0, 1,..., of a compact operator, and particularly a compact Hankel operator =[hj+k-1], converges monotonically to zero. Since the (n + 1)st s-number sn measures the error of L(|z|=1) approximation, modulo an additive H function, by nth degree proper rational functions whose poles are restricted to |z| < 1, it is very important to study how fast {sn} converges to zero. It is not difficult to see that if hn=O(n-), for some > 1, then sn=O(n-). In this paper we construct, for any given sequence e{open}n 0, a compact Hankel operator such that sne{open}n for all n. 1992 Birkhuser.

ON THE CONVERGENCE RATE OF S-NUMBERS OF COMPACT HANKEL-OPERATORS Academic Article