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ON SMALL SUBSPACE LATTICES IN HILBERT SPACE

Published online by Cambridge University Press:  15 October 2013

AIJU DONG
Affiliation:
College of Mathematics and Computer Engineering, Xi’an University of Arts and Science, Xi’an 710065, PR China email [email protected]
WENMING WU*
Affiliation:
College of Mathematics, Chongqing Normal University, Chongqing 400047, PR China
WEI YUAN
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100190, PR China email [email protected]
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Abstract

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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.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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