Perturbation analysis for the operator equation Tx=b in Banach spaces

[摘要] Let X-1, X-2 be two Banach spaces over the complex field C and let T: X-1 --> X-2 be a bounded linear operator with the generalized inverse T+. Let (T) over bar = T + delta T be a bounded linear operator with \\T+\\ \\delta T\\ < 1 Suppose that dim ker (T) over bar = dim ker T < infinity or R((T) over bar) boolean AND Ker T+ = 0. Then (T) over bar has the generalized inverse <(T)over bar(+)> = (I + T+ delta T)(-1) T+ with \\<(T)over bar(+)>\\ less than or equal to \\T+\\/1-\\T+\\ \\delta T\\. This result generalizes Theorem 3.9 of M. Z. Nashed (''Generalized Inverses and Applications,'' Academic Press, New York, 1976). Using this result, we give some results of the perturbation analysis for the operator equation Tx = b. (C) 1997 Academic Press.

[发布日期] 1997-08-01