About Nearstandardness in Hilbert Space

Author: Lyantse W.E.   Kudryk T.S.  

Publisher: Springer Publishing Company

ISSN: 0037-4466

Source: Siberian Mathematical Journal, Vol.43, Iss.5, 2002-09, pp. : 868-881

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

The notions of nearstandardness and shadow are generalizations of convergence and limit respectively. There exist many useful variants of these notions. Here we collect some special aspects and properties of shadows and nearstandardness. This paper concerns the following: the shadows of a vector and an operator, weak, strong, and uniform nearstandardness, use of the Hilbert–Schmidt norm, properties of the map A°A, nearstandard projections and subspaces, conditions for graph-nearstandardness, and examples. We work with IST, i.e. Internal Set Theory, a version of nonstandard analysis suggested by Edward Nelson.