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The Universal Factorization Property for Commutative Subspace Lattices

In: Algebraic Methods in Operator Theory

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  • John Daughtry

    (East Carolina University, Department of Mathematics)

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.

Suggested Citation

  • John Daughtry, 1994. "The Universal Factorization Property for Commutative Subspace Lattices," Springer Books, in: Raúl E. Curto & Palle E. T. Jørgensen (ed.), Algebraic Methods in Operator Theory, pages 59-65, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0255-4_8
    DOI: 10.1007/978-1-4612-0255-4_8
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