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Non-reflexive double triangles

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

W. E. Longstaff
W. E. Longstaff
Affiliation:
Department of MathematicsUniversity of Western AustraliaNedlands, Western Australia6009
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Abstract

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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.

MSC classification

Secondary: 47A15: Invariant subspaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 3 , December 1983 , pp. 349 - 356
Copyright
Copyright © Australian Mathematical Society 1983

References

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