ON SMALL SUBSPACE LATTICES IN HILBERT SPACE

被引：4

作者：

Dong, Aiju ^{[1
]}

Wu, Wenming ^{[2
]}

Yuan, Wei ^{[3
]}

机构：

[1] Xian Univ Arts & Sci, Coll Math & Comp Engn, Xian 710065, Peoples R China

[2] Chongqing Normal Univ, Coll Math, Chongqing 400047, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2014年 / 96卷 / 01期

关键词：

projections; lattice; double triangle; reflexive; transitive; KADISON-SINGER ALGEBRAS;

D O I：

10.1017/S1446788713000384

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the reflexivity and transitivity of a double triangle lattice of subspaces in a Hilbert space. We show that the double triangle lattice is neither reflexive nor transitive when some invertibility condition is satisfied (by the restriction of a projection under another). In this case, we show that the reflexive lattice determined by the double triangle lattice contains infinitely many projections, which partially answers a problem of Halmos on small lattices of subspaces in Hilbert spaces.

引用

页码：44 / 60

页数：17

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