ASYMPTOTIC MOORE-PENROSE INVERSION OF TOEPLITZ-OPERATORS

We give the complete solution of a problem which reads in its simplest form as follows: Let T(a) be a block Toeplitz operator with piecewise continuous generating function and A(n):= T-n(a) be the finite sectio ns of this operator. Describe all sequences {B-n} belonging to the alg ebra A which is generated by all the sequences {T-n(a)} with a piecewi se continuous, and fulfilling the conditions {A(n)B(n) A(n) - A(n)} is an element of G, {B(n)A(n)B(n) - B-n} is an element of G, {(B(n)A(n)) - B(n)A(n)} is an element of G, {(A(n)B(n))* - A(n)B(n)} is an eleme nt of G, where G subset of A denotes the collection of all sequences ( C-n) with parallel to C-n parallel to --> 0 as n tends to infinity, an d T(a) is supposed to be Fredholm. (C) Elsevier Science Inc., 1997.