Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality. Particular cases are Dirac-Coulomb operators where distinguished selfadjoint extensions are obtained for the optimal range of coupling constants.

In L 2 ( R 3 ; C ) , we consider a selfadjoint operator ? > 0 given by the differential expression ? ? 1 / curl ? x ? ? div where is constant positive matrix, matrix-valued function and real-valued are periodic with respect to some lattice, definite bounded. We study behavior of operator-valued functions cos ? ? sin for ? small . It shown that these operators converge corresponding in norm acti...

We study spectral asymptotics for small non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part possesses several invariant Lagrangian tori enjoying a Diophantine property. We get complete asymptotic expansions for all eigenvalues in certain rectangles in the complex plane in two different cases: in the...

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...

Non-commutative multi-variable versions of weighted shifts arise naturally as ‘weighted’ left creation operators acting on Fock space. We investigate the unital wot-closed algebras they generate. The unweighted case yields non-commutative analytic Toeplitz algebras. The commutant can be described in terms of weighted right creation operators when the weights satisfy a condition specific to the ...