An algebraic characterization of Hilbert lattices
V. Capraro
TL;DR
This paper provides an algebraic framework to characterize the lattice of projections in matrix algebras and extends this characterization to bounded operators on separable Hilbert spaces.
Contribution
It introduces a novel algebraic approach to describe Hilbert lattices, broadening understanding from finite-dimensional matrices to infinite-dimensional operators.
Findings
Algebraic characterization of projections in M_n(C)
Extension of the characterization to B(H) for separable H
New insights into the structure of Hilbert lattices
Abstract
In this paper we give an algebraic characterization of the projections lattice of and we extend it to the case of , with separable Hilbert space.
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Taxonomy
TopicsAdvanced Algebra and Logic · Mathematical Analysis and Transform Methods · Mathematical Dynamics and Fractals