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Title: | Quasi-splitting subspaces in a pre-Hilbert space |
Authors: | Buhagiar, David Chetcuti, Emanuel |
Keywords: | Hilbert space Lattice theory Invariant subspaces Algebra, Boolean |
Issue Date: | 2007-03 |
Publisher: | Wiley-VCH |
Citation: | Buhagiar, D., & Chetcuti, E. (2007). Quasi-splitting subspaces in a pre-Hilbert space. Mathematische Nachrichten, 280(5-6), 479-484. |
Abstract: | Let S be a pre-Hilbert space. Two classes of closed subspaces of S that can naturally replace the lattice of projections in a Hilbert space are E (S) and F (S), the classes of splitting subspaces and orthogonally closed subspaces of S respectively. It is well-known that in general the algebraic structure of E (S) differs considerably from that of F (S) and the two coalesce if and only if S is a Hilbert space. In the present note we introduce the class Eq(S) of quasi-splitting subspaces of S. First it is shown that Eq(S) falls between E (S) and F (S). It is also shown that, in contrast to the other two classes, Eq(S) can sometimes be a complete lattice (without S being complete) and yet, in other examples Eq(S) is not a lattice. At the end, the algebraic structure of Eq(S) is used to characterize Hilbert spaces. |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/18435 |
Appears in Collections: | Scholarly Works - FacSciMat |
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Quasi‐splitting subspaces in a pre‐Hilbert space.pdf Restricted Access | Quasi-splitting subspaces in a pre-Hilbert space | 126.37 kB | Adobe PDF | View/Open Request a copy |
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