Defect basis property of the eigenvectors of a selfadjoint operator-valued function and formula for defect

A continuous selfadjoint operator-valued functionA(x) is considered. Possible changes of dimension of the positive partA₊(t) are investigated ast transverses through some Fredholm eigenvalue ₀ . Some results on defect basis property are obtained, and the formula for the defect is proved. Both holomorphic and non-holomorphic cases are considered.