Scalar operators and integration

Journal of the Australian Mathematical Society

Igor Kluvánek¹ 

关键词: 46 G 10;    47 B 40;    47 D 30;    443 A 22;   

DOI  :  10.1017/S1446788700031116

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The notion of a scalar operator on a Banach space, in the sense of N. Dunford, is widened so as to cover those operators which can be approximated in the operator norm by linear combinations of disjoint values of an additive and multiplicative operator valued set function, P, on an algebra of sets in a space Ω such that P(Ω) = I, subject to some conditions guaranteeing that this definition is unambiguous. An operator T turns out to be scalar in this sense, if and only if, there exists a (not necessarily bounded) Boolean algebra of bounded projections such that the Banach algebra of operators it generates is semisimple and contains T.

【 授权许可】

Unknown