UNIVERSITY
OF WROCŁAW
 
Main Page
Contents of previous volumes
Forthcoming papers
General Information
Instructions for authors


VOLUMES
38.2 38.1 37.2 37.1 36.2 36.1 35.2
35.1 34.2 34.1 33.2 33.1 32.2 32.1
31.2 31.1 30.2 30.1 29.2 29.1 28.2
28.1 27.2 27.1 26.2 26.1 25.2 25.1
24.2 24.1 23.2 23.1 22.2 22.1 21.2
21.1 20.2 20.1 19.2 19.1 18.2 18.1
17.2 17.1 16.2 16.1 15 14.2 14.1
13.2 13.1 12.2 12.1 11.2 11.1 10.2
10.1 9.2 9.1 8 7.2 7.1 6.2
6.1 5.2 5.1 4.2 4.1 3.2 3.1
2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 34, Fasc. 1,
pages 147 - 159
 

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

Hiroshi Ando
Izumi Ojima
Hayato Saigo

Abstract: Let ω ∈ βℕ\ 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
  ω  of a self-adjoint operator A . In this note, we give an alternative description of A
  ω  and the Hilbert space H (A ) on which A
  ω  is densely defined. This provides a criterion to determine a representing sequence (ξ )
  n n  of a given vector ξ ∈ dom (A )
         ω which has the property that A  ξ = (A ξ)
  ω      n ω  holds. An explicit core for A
  ω  is also described.

2000 AMS Mathematics Subject Classification: Primary: 47A10; Secondary: 03C20.

Keywords and phrases: Ultraproduct, unbounded self-adjoint operators.

Download:    Abstract    Full text   Abstract + References