Abstract :
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 An colon, equals Tn(a) be the finite sections of this operator. Describe all sequences Bn belonging to the algebra & which is generated by all the sequences Tn(a) with a piecewise continuous, and fulfilling the conditions AnBnAn – An set membership, variant G, BnAnBn − Bn set membership, variant G, (BnAn)* − BnAn set membership, variant G, (AnBn)* − AnBn set membership, variant G, where G subset of & denotes the collection of all sequences (Cn) with Cn → 0 as n tends to infinity, and T(a) is supposed to be Fredholm. 1997
