Krein space operator-theoretic methods are used to prove that the operator (sgn x) d is similar to a selfadjoint operator in the Hilbert space L2 (R) . Let L be a symmetric ordinary differential expression. Spectral properties of the operators associated with the weighted eigenvalue problem Lu = )wu have been studied extensively. When w is positive, this problem leads to a selfadjoint problem i...

We characterize the essentially normal composition operators induced on the Hardy space H2 by linear fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic non-automorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition we characterize those linearfractionally induced compositi...

Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugatelinear symmetric operators...

A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation properties of the form sum extension are observed.

We extend Akemann, Anderson, and Weaver’s Spectral Scale definition to include selfadjoint operators from semifinite von Neumann algebras. New illustrations of spectral scales in both the finite and semifinite von Neumann settings are presented. A counterexample to a conjecture made by Akemann concerning normal operators and the geometry of the their perspective spectral scales in the finite se...

It is shown that the operators associated with the perturbed wave equation in IR n and with the elliptic operators with an indeenite weight function and mildly varying coeecients on IR n are similar to a selfadjoint operator in a Hilbert space. These operators have the whole IR as the spectrum. It is shown that they are positive operators in corresponding Krein spaces, and the whole problem is ...

We consider the Dirac equation with a magnetic-solenoid field (the superposition of a solenoid field and a collinear uniform magnetic field). Using von Neumann’s theory of the selfadjoint extensions of symmetric operators, we construct selfadjoint Dirac Hamiltonians for the case of the Aharonov-Bohm solenoid in 2 + 1 and 3 + 1 dimensions. Each extension of the family is specified by certain asy...

For bounded linear operators A,B on a Hilbert space H we show the validity of the estimate ∑ λ∈σd(B) dist(λ,Num(A)) ≤ ‖B −A‖pSp , p ≥ 1, and apply it to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schrödinger operators.

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...

Abstract An estimate for the norm of selfadjoint Toeplitz operators with a radial, bounded and integrable symbol is obtained. This emphasizes fact that such operator strictly less than supremum symbol. Consequences time-frequency localization are also given.