Abstract:

A new generalized BottDuffin(BD) inverse, named the second kind of generalized BottDuffin inverse of bounded linear operator A on an infinite dimensional Hilbert space with respect to a closed subspace L, is defined by using ｛1｝inverse of operators, which is a generalization of the second kind of generalized BottDuffin inverse of matrices. Also, the existence, the representations and some properties of the second kind of generalized BottDuffin inverse are discussed by applying the technique of block operator matrix.

Key words: generalized BottDuffin inverse; ｛1｝inverse; MoorePenrose inverse; block operator