This PhD thesis on Pure Mathematics investigates properties of subspace lattices related to reflexivity. The research focuses on issues such as the reflexivity of the tensor product of two reflexive lattices, the lattice tensor product formula and property (p). Besides, the research investigates other properties related to subspace lattiees such as semi-strong closedness and compactness, and studies algebras associated to certain classes of subspace lattices. The work is divided into three research sections focused on a) the lattice tensor product formula, reflexivity of subspace lattices and property (P) where the author has mainly worked with subspace lattices having the ultraweak rank one density property, atomic Boolean subspace lattices and commutative subspace lattices, b) the behaviour of properties of subspace lattices such as reflexivity, semi-strong closedness and compactness when tensoring with other subspace lattices and c) algebras associated to various subspace lattices. This thesis attributes on our understanding of property (P) by showing that property (P) holds for a number of subspace lattices. Examples of algebras where the lattice tensor product formula holds and of subspace lattices that are reflexive are presented. In addition, our knowledge on semi-strong closedness and compactness of subspace lattices is developed and a partial description of algebras associated to a class of subspace lattices is obtained.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:557886 |
| Date | January 2011 |
| Creators | Papapanayides, Sawas |
| Publisher | Queen's University Belfast |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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