We fix a logical connection (Stone Pred : Set op −→ BA given by 2 as a schizophrenic object) and study coalgebraic modal logic that is induced by a functor T : Set −→ Set which is finitary, standard, preserves weak pullbacks and finite sets. We prove that for any such T , the cover modality nabla is a left (and its dual delta is a right) adjoint relative to Pω. We then consider monotone unary m...

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 ...

In this paper, we study Dirichlet operators on certain smooth Banach spaces. We establish the well-known Kato's inequality in our general infinite dimensional setting. By applying this,we show the essential self-adjointness of Dirichlet operators with non-constant diffusion part on certain smooth Banach spaces. We also provide an approximation criterion for essential self-adjointness of Dirichl...

We derive Povzner–Wienholtz-type self-adjointness results form× m matrix-valued Sturm–Liouville operators T = R [

We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lat...

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, latter being not necessarily involutive. discuss extension theory, refined polar and singular-value decompositions, antilinear eigenfunction expansions. The study is motivated by physical symmetries quantum mechanics with non-self-adjoint operators.

An implication operator A is said to be tied if there is a binary operation T that ties A; that is, the identity A(a,A(b, z)) = A(T (a, b), z) holds for all a, b, z. We aim at the construction of a complete predicate logic for prelinear tied adjointness algebras. We realize this in three steps. In the first step, we establish a propositional calculus AdjTPC, complete for the class of all tied a...

Introduction 2 1. Self-adjointness of Schrödinger operators 3 1.0. Solving the Schrödinger equation 3 1.1. Linear operators in Hilbert space 7 1.2. Criteria for (essential) self-adjointness 13 1.3. Application to Schrödinger operators 18 2. Hardy-Rellich inequalities 21 2.0. Relative boundedness 21 2.1. Weighted estimates 24 2.2. Explicit bounds 26 3. Spectral properties of radially periodic Sc...