The second kind of generalized Bott-Duffin inverse of operators

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.