Numerical ranges in locally M-convex algebras. I

Journal of the Australian Mathematical Society

Thanassis Chryssakis¹ 

关键词: 46 H 99;    46 K 99;   

DOI  :  10.1017/S1446788700033747

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The bidualof a unital infrabarrelled l.m.c. C* algebra E, equipped with the bidual topology and the regualr Arens product, is always an l.m.c. C*-algebra. On the other hand, a unital l.m.c. *-algebra E has the C*-property if and only if every self-adjoint element x of E is strongly hermitian (x has real numerical range), or the sets of normalized states and normalized continuous positive linear forms of E coincide. Finally, every unital cpmplete l.m.c. C* algebra satisfying, locally, the property ‘the extreme points are dense in that set of continuous positive linear forms” (antiliminal algebra) has the complexes as its only normal elements.

【 授权许可】

Unknown