Extensions of symmetric operators I: The inner characteristic function case

• Autorzy: R.T.W. Martin
• Języki publikacji: EN

Abstrakty

EN

Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.

Słowa kluczowe

EN

symmetric operators; partial isometries; self-adjoint and unitary extensions; reproducing kernelHilbert spaces of analytic functions; Hardy and deBranges Rovnyak spaces; Livšic characteristic function

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2015-04-01

zaakceptowano

2015-06-16

online

2015-07-10

Twórcy

autor

R.T.W. Martin

• University of Cape Town, Rondebosch, 7701 Cape Town, South Africa

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Identyfikatory

DOI

10.1515/conop-2015-0004