Abstract In the context of a geodesically complete Riemannian manifold M , we study self‐adjointness where ∇ is metric covariant derivative (with formal adjoint ) on Hermitian vector bundle over and V locally square integrable section such that (fiberwise) norm “negative” part belongs to local Kato class (or, more generally, contractive Dynkin class). Instead lower semiboundedness hypothesis, a...

We study topological properties of the correspondence of prime spectra associated to a noncommutative ring homomorphism R → S. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski closed subsets of SpecR and SpecS; these functors arise naturally from restriction and extension of scalars. When R and S are left noetherian, adjointness occurs ...

We provide a shorter and more transparent proof of a result by I. Oleinik 25, 26, 27]. It gives a suucient condition of the essential self-adjointness of a Schrr odinger operator on a non-compact Riemannian manifold with a locally bounded potential in terms of the completeness of the dynamics for a related classical system. The simpliication of the proof given by I. Oleinik is achieved by an ex...

Distinguished selfadjoint extension of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, −|x|. The method uses Hardy-Dirac inequalities and quadratic form techniques.

The Dirac equation for a massive spin-12 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V . The second-order equations for the radial parts of the spinor wave function are shown to involve a squared Dirac operator for the free case, whose essential self-adjointness is proved by using the Weyl limit point-limit circle criterion, and a...

We consider perturbed quadharmonic operators, ? 4 + V , acting on sections of a Hermitian vector bundle over complete Riemannian manifold, with the potential satisfying bound from below by non-positive function depending distance point. Under bounded geometry assumption and underlying we give sufficient condition for essential self-adjointness such operators. then apply this to prove separation...

1. Topological Vector Spaces 1 1.1. The Krein-Milman theorem 7 2. Banach Algebras 11 2.1. Commutative Banach algebras 14 2.2. ∗–Algebras (over complexes) 17 2.3. Exercises 20 3. The Spectral Theorem 21 3.1. Problems on the Spectral Theorem (Multiplication Operator Form) 26 3.2. Integration with respect to a Projection Valued Measure 27 3.3. The Functional Calculus 34 4. Unbounded Operators 37 4...

1. Topological Vector Spaces 1 1.1. The Krein-Milman theorem 7 2. Banach Algebras 11 2.1. Commutative Banach algebras 14 2.2. ∗–Algebras (over complexes) 17 2.3. Problems on Banach algebras 20 3. The Spectral Theorem 21 3.1. Problems on the Spectral Theorem (Multiplication Operator Form) 26 3.2. Integration with respect to a Projection Valued Measure 27 3.3. The Functional Calculus 34 4. Unboun...

The observable algebra O of SOq(3)-symmetric quantum mechanics is generated by the coordinates Pi and Xi of momentum and position spaces (which are both isomorphic to the SOq(3)-covariant real quantum space IR 3 q). Their interrelations are determined with the quantum group covariant differential calculus. For a quantum mechanical representation of O on a Hilbert space essential self-adjointnes...

‘One universe, one logic’ takes the world as it is and leads to adjointness as the global logic of anything. The alternative approach to find a unification of known logics requires assumptions and is therefore consistent with the same conclusion for a universal logic has to be universally applicable. The universal characteristic of adjointness is that it has a natural construction from the conc...