NOTES ON THE KRUPA-ZAWISZA ULTRAPOWER OF SELF-ADJOINT OPERATORS

作者：Ando Hiroshi^*; Ojima Izumi; Saigo Hayato

来源：Probability and Mathematical Statistics, 2014, 34(1): 147-159.

• Ultraproduct
• unbounded self-adjoint operators

Let w is an element of beta N \ N be a free ultrafilter on N. 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(w) of a self-adjoint operator A. In this note, we give an alternative description of A(w) and the Hilbert space H (A) on which A(w) is densely defined. This provides a criterion to determine a representing sequence (xi n)(n) of a given vector xi is an element of dom (A(w)) which has the property that A(w)xi = (A xi(n))(w) holds. An explicit core for A(w) is also described.

• 出版日期2014