M. Bakonyi et Hj. Woerdeman, EXTENSIONS OF POSITIVE-DEFINITE FREDHOLM OPERATORS WITH PARTIALLY ZERO INVERSE, Mathematische Nachrichten, 193, 1998, pp. 5-18
Considered is the problem of adjusting a positive definite operator in
order to obtain a partially zero inverse. Using generalized determina
nts the problem is settled for operator matrices with Hilbert Schmidt
off diagonal entries. For Fredholm integral operators an approximation
result is obtained.