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Journal of Operator Theory

Volume 65, Issue 1, Winter 2011  pp. 115-129.

Domination and commutativity in Pontryagin spaces

Authors:  Michal Wojtylak
Author institution: Jagiellonian University, Faculty of Mathematics and Computer Science, Lojasiewicza 6, 30--348 Krakow, Poland

Summary:  We show a sufficient condition for selfadjointness and spectral commutation of a system of unbounded symmetric operators in a Pontryagin space. The main concepts are domination and the set of bounded vectors of an operator. We investigate also operator matrices with unbounded entries and prove a Pontryagin space version of the Nelson's criterion.

Keywords:  Symmetric operator, Pontryagin space, operator matrix

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