A factorization of extremal extensions with applications to block operator matrices

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.129, Iss.1-2, 2010-10, pp. : 112-141

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Abstract

For a nonnegative operator KC in a Hilbert space H we give a description of all extremal extensions by means of the factors K and C. In particular, we discuss the Friedrichs and the Kren-von Neumann extension of KC. Applications to systems of differential operators where these extensions are characterized via boundary conditions are presented as well.

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