A factorization of extremal extensions with applications to block operator matrices

Authors: Förster, K.¹; Nafalska, M.²

Source: Acta Mathematica Hungarica, Volume 129, Numbers 1-2, October 2010 , pp. 112-141(30)

Publisher: Springer

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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.

Keywords: Friedrichs extension; Kren-von Neumann extension; extremal extension; factorization; block operator matrix; primary 47B25; secondary 47A20

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10474-010-9248-x

Affiliations: 1: Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany, Email: foerster@math.tu-berlin.de 2: Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany, Email: nafalska@math.tu-berlin.de

Publication date: 2010-10-01