Perturbations AT of a selfadjoint operator A by symmetric finite rank operators T from H2(A) to H−2(A) are studied. The finite dimensional family of selfadjoint extensions determined by AT is given explicitly.

Krein space operator-theoretic methods are used to prove that the operator (sgnx)-j-j is similar to a selfadjoint operator in the Hubert space ¿2(R) • Let L be a symmetric ordinary differential expression. Spectral properties of the operators associated with the weighted eigenvalue problem Lu = Xwu have been studied extensively. When w is positive, this problem leads to a selfadjoint problem in...

For a symmetric linear compact resp. densely defined operator with inverse, expansion theorems in series of eigenvectors are known. The aim the present paper is to generalize known case corresponding operators without symmetry property. this, we replace set orthonormal by biorthonormal principal vectors simple eigenvalues general eigenvalues. results for property all new. Furthermore, if symmet...