Relatively central operators on Archimedean vector lattices II

Journal of the Australian Mathematical Society

P. T. N. McPolin¹ 

[1] A. W. Wickstead

关键词: 47 B 55;    47 A 10;    46 A 40;   

DOI  :  10.1017/S144678870002752X

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We continue the study of operators from an Archimedean vector lattice E into a cofinal sublattice H which have the property that there is λ > 0 such that if x ∈ E, h ∈ H and |x|≤|h|, then |Tx| ≤ λ|h|. The collection Z(E|H) of all of those operators forms an algebra under composition. We investigate the relationship between the properties of having an identity, being Abelin and being semi-simple for such-algebras, culminating in a proof that they are equivalent if H is Dedekind complete. We also study various for such an operator T, showing that, apart from 0, its spectrum relative to Z(E|H) is the same as that of T|H relative to Z(H) and that of T relative to ℒ(E) (Provided E is a Banach lattice and H is closed).

【 授权许可】

Unknown