NOTES ON THE KRUPA–ZAWISZA ULTRAPOWER OF SELF-ADJOINTOPERATORS

Hiroshi Ando Izumi Ojima Hayato Saigo

Abstract: Let be a free ultrafilter on . 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 of a self-adjoint operator . In this note, we give an alternative
description of and the Hilbert space on which is densely defined. This
provides a criterion to determine a representing sequence of a given vector
which has the property that holds. An explicit core for
is also described.