Reflexive index of a family of subspaces

Authors

  • W. E. Longstaff Unaffiliated - recently retired university professor (see bio)

Keywords:

reflexive, subspace, invariant

Abstract

A definition of the reflexive index of a family of (closed) subspaces of a complex, separable Hilbert space H is given, analogous to one given by D. Zhao for a family of subsets of a set. Following some observations, some examples are given, including: (a) a subspace lattice on H with precisely five nontrivial elements with infinite reflexive index; (b) a reflexive subspace lattice on H with infinite reflexive index; (c) for each positive integer n satisfying dim H≥n+1, a reflexive subspace lattice on H with reflexive index n. If H is infinite-dimensional and B is an atomic Boolean algebra subspace lattice on H with n equidimensional atoms and with the property that the vector sum K+L is closed, for every K,L∈B, then B has reflexive index at most n. DOI: 10.1017/S0004972713001159

Author Biography

W. E. Longstaff, Unaffiliated - recently retired university professor (see bio)

Retired three years ago from position of Professor of Mathematics, School of Maths. & Stats., University of Western Australia. Served UWA for 35 years.

Published

2014-06-03

Issue

Vol. 90 No. 1 (2014)

Section

Articles
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