THE ALGEBRA OF DECOMPOSABLE OPERATORS IN DIRECT INTEGRALS OF NOT NECESSARILY SEPARABLE HILBERT-SPACES

被引：3

作者：

SCHAFLITZEL, R

机构：

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1990年 / 110卷 / 04期

关键词：

DIRECT INTEGRALS; ALGEBRA OF DECOMPOSABLE OPERATORS; ALGEBRA OF DIAGONALIZABLE OPERATORS; CONTINUUM-HYPOTHESIS;

D O I：

10.2307/2047746

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Considering direct integrals of not necessarily separable Hilbert spaces we examine the question whether the algebra of decomposable operators is the commutant of the algebra of diagonalizable operators. Using the continuum-hypothesis we prove this relation, if the set of square integrable vector fields is generated by a subset-GAMMA-0 such that \GAMMA-0\ less-than-or-equal-to \R\. For the general case, a counterexample is given.

引用

页码：983 / 987

页数：5