Let H=H+⊕H− be an orthogonal decomposition of a Hilbert space, with E+, E− the corresponding projections. Let A be a selfadjoint operator in H which is codiagonal with respect to this decomposition (i.e. A(H+)⊂H− and ...

Given a bounded selfadjoint operator a in a Hilbert space H, the aim of this paper is to study the orbit of a, i.e., the set of operators which are congruent to a. We establish some necessary and sufficient conditions for ...

Let H be a Hilbert space and L(H) be the algebra of all bounded linear operators from H to H. Our goal in this article is to study the set P⋅Lh of operators in L(H) that can be factorized as the product of an orthogonal ...

Given a linear bounded selfadjoint operator a on a complex separable Hilbert space H, we study the decompositions of a as a difference of two positive operators whose ranges satisfy an angle condition. These decompositions ...

We present some simple arguments to show that quantum mechanics operators are required to be self-adjoint. We emphasize that the very definition of a self-adjoint operator includes the prescription of a certain domain of ...

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the ...

Given a Hilbert space (H, ⟨ , ⟩) and a bounded selfadjoint operator B consider the sesquilinear form over H induced by B, ⟨ x , y ⟩_B=?Bx,y?, x,y ∈ H. A bounded operator T is B-selfadjoint if it is selfadjoint respect to ...

We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar delta-shell boundary conditions, on piecewise C-2 domains (with finitely many corners). For both models, we ...

The space G^+ of postive invertible operators of a C*-algebra A, with the appropriate Finsler metric, behaves like a (non positively curved)symmetric space. Among the characteristic properties of such spaces, one has that ...