Notes on the Krupa-Zawisza Ultrapower of Self-Adjoint Operators

2013/05/08 by Ando, Hiroshi, Ojima, Izumi, Saigo, Hayato
#03C20 #47A10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1305.1827

Abstract

It is known that there is a difficulty in constructing the ultrapower of unbounded operators. Krupa and Zawisza gave a rigorous definition of the ultrapower A^omega of a selfadjoint operator A. In this note, we give alternative description of A^omega and the Hilbert space H(A) on which A^omega is densely defined, which provides a criterion to determine to which representing sequence (ξ_n)n of a given vector ξin dom(A^omega) has the property that A^omegaξ= (Aξ_n)_omega holds.

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