The Universal Factorization Property for Commutative Subspace Lattices

John Daughtry ()
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John Daughtry: East Carolina University, Department of Mathematics

A chapter in Algebraic Methods in Operator Theory, 1994, pp 59-65 from Springer

Abstract: Abstract We present a necessary and sufficient condition for a commutative subspace lattice (CSL) to have the property that every sublattice has the universal factorization property (UFP). Then we derive a sufficient condition for a CSL to have the UFP which applies to all known examples of CSL’s with the UFP. (The preceding results are, in fact, obtained for CSL- subalgebras of factor von Neumann algebras.) Finally, we give an example of a CSL which has the UFP, even though it is not a direct sum of a complemented lattice and a CSL with the property that every linearly ordered sublattice is countable.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0255-4_8

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DOI: 10.1007/978-1-4612-0255-4_8

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