The Closed Extensions of a Closed Operator

Pseudo Algebraically Closed Extensions

Closed Commutants of the Backward Shift Operator

We characterize the closed operators with domain contained in the Hardy space H 2 that commute with the backward shift. Also, we give necessary and suucient conditions for such an operator to be a Toeplitz operator with symbol the complex conjugate of a function in H 2. In particular, we show that this fact depends only on the domain. Introduction. Let F be a function in the Hardy space of the ...

On Pseudo Algebraically Closed Extensions of Fields

The notion of ‘Pseudo Algebraically Closed (PAC) extensions’ is a generalization of the classical notion of PAC fields. In this work we develop a basic machinery to study PAC extensions. This machinery is based on a generalization of embedding problems to field extensions. The main goal is to prove that the Galois closure of any proper separable algebraic PAC extension is its separable closure....

Existentially Closed R-domains in Regular Extensions

Functional Model of a Closed Non-selfadjoint Operator

We construct the symmetric functional model for an arbitrary closed operator with a non-empty resolvent set acting on a separable Hilbert space. The main techniques of the study are based on the explicit form of the Sz.-Nagy-Foiaş model for a closed dissipative operator, the Potapov-Ginzburg transform of characteristic functions, and certain resolvent identities. All considerations are carried ...