On the Expression of Generalized Inverses of Perturbed Bounded Linear Operators

Document Type

Article

Publication Date

1-1-2003

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

Let X and Y be two Hilbert spaces or Banach spaces, and let T: X → Y be a bounded linear operator with closed range. Let T̃ = T + δT with ∥δT∥∥T∥ < 1. We give some equivalent conditions for the generalized inverse of T̃ to have the simplest expression T̃† = (I + T†δT) -1T† = T†(I + δTT †)-1.

Publication Title

Missouri Journal of Mathematical Sciences

Volume

15

Issue

1

First Page

1

Last Page

8

Link to Full Text

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