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Lattice Operators and Topologies [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 Working within a complete (not necessarily atomic) Boolean algebra, we use a sublattice to define a topology on that algebra. Our operators generalize complement on a lattice which in turn abstracts the set theoretic operator.
Eva Cogan
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Operators in finite distributive subspace lattices II [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 1994 AbstractThe purpose of this paper is to settle in the negative an open problem in operator theory, which asks whether in a finite distributive subspace lattice ℒ on a Hilbert space, every finite rank operator of Alg ℒ can be written as a finite sum of rank one operators from Alg ℒ.
N. K. Spanoudakis
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Operator Hyperreflexivity of Subspace Lattices [PDF]
Integral Equations and Operator Theory, 2010 Given a (complex) Hilbert space \({\mathcal H}\), a subspace lattice \({\mathcal L}\) is a collection of orthogonal projections onto subspaces of \({\mathcal H}\) such that \({\mathcal L}\) contains \(0\) and the identity projection \(I\) and is closed in the strong operator topology.
Janko Bračič +3 more
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CHIRAL FERMION OPERATORS ON THE LATTICE [PDF]
International Journal of Modern Physics A, 2003 We only require generalized chiral symmetry and γ5-hermiticity, which leads to a large class of Dirac operators describing massless fermions on the lattice, and use this framework to give an overview of developments in this field. Spectral representations turn out to be a powerful tool for obtaining detailed properties of the operators and a general ...
Werner Kerler
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Operators on complemented lattices [PDF]
Soft ComputingAbstract The present paper deals with complemented lattices where, however, a unary operation of complementation is not explicitly assumed. This means that an element can have several complements. The mapping $$^+$$
Ivan Chajda, Helmut Länger
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Instanton density operator in lattice QCD from higher category theory [PDF]
SciPost PhysicsA natural definition for instanton density operator in lattice QCD has long been desired. We show this problem is, and has to be, solved by higher category theory.
Jing-Yuan Chen
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Integral Operators on Lattices [PDF]
Order, 2022 This paper introduces the notion of integral operators on lattices and studies their role in understanding lattices, their classification and their derived structures. As is well known, the derivation, or differential operator, and integral operator are fundamental in analysis and its broad applications.
Aiping Gan, Li Guo, Shoufeng Wang
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The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems
Complexity, 2021 Following the idea of L-fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L-fuzzy generalized neighborhood systems. In particular, as
Qiao-Ling Song +5 more
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On the Lattice Properties of Almost L-Weakly and Almost M-Weakly Compact Operators
Journal of Function Spaces, 2021 We establish the domination property and some lattice approximation properties for almost L-weakly and almost M-weakly compact operators. Then, we consider the linear span of positive almost L-weakly (resp., almost M-weakly) compact operators and give ...
Barış Akay, Ömer Gök
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Atomic Operators in Vector Lattices [PDF]
Mediterranean Journal of Mathematics, 2020 AbstractIn this paper, we introduce a new class of operators on vector lattices. We say that a linear or nonlinear operator T from a vector lattice E to a vector lattice F is atomic if there exists a Boolean homomorphism $$\Phi $$ Φ from the Boolean algebra $${\mathfrak {B}}(E)$$ B ( E ) of all order projections on E to $${\mathfrak {B}}(F)$$ B ...
Ralph Chill, Marat Pliev
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