arXiv Analytics

Sign in

arXiv:1305.1827 [math.FA]AbstractReferencesReviewsResources

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

Hiroshi Ando, Izumi Ojima, Hayato Saigo

Published 2013-05-08Version 1

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 (\xi_n)n of a given vector \xi in dom(A^{omega}) has the property that A^{omega}\xi = (A\xi_n)_{omega} holds.

Comments: 13pages
Categories: math.FA
Subjects: 47A10, 03C20
Related articles: Most relevant | Search more
arXiv:1309.1219 [math.FA] (Published 2013-09-05, updated 2013-09-15)
Frames of subspaces in Hilbert spaces with $W$-metrics
arXiv:1308.6420 [math.FA] (Published 2013-08-29, updated 2013-12-14)
Avoiding σ-porous sets in Hilbert spaces
arXiv:1211.2127 [math.FA] (Published 2012-11-06, updated 2014-06-11)
The splitting lemmas for nonsmooth functionals on Hilbert spaces I

Links

Toolbox