Non-reflexive double triangles

Journal of the Australian Mathematical Society

W. E. Longstaff¹ 

关键词: primary 47 A 15;    secondary 06 A 20;   

DOI  :  10.1017/S144678870002704X

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

A double triangle subspace lattice in a Hilbert space H is a 5-element set of subspaces of H, containing (0) and H, with each pair of non-trivial elements intersecting in (0) and spanning H. It is shown that if any pair of non-trivial elements has a closed vector sum the double triangle is both non-reflexive and non-transitive. A double triangle in H⊕H is an operator double triangle if each non-trivial elements is the graph of an operator acting on H. A sufficient condition is given for any operator double triangle to be non-reflexive.

【 授权许可】

Unknown