Vector lattices in synaptic algebras
-
David J. Foulis
,
Anna Jenčová
Abstract
A synaptic algebra A is a generalization of the self-adjoint part of a von Neumann algebra. We study a linear subspace V of A in regard to the question of when V is a vector lattice. Our main theorem states that if V contains the identity element of A and is closed under the formation of both the absolute value and the carrier of its elements, then V is a vector lattice if and only if the elements of V commute pairwise.
The second and third authors were supported by grant VEGA 2/0069/16.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Paolo de Lucia
- Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
- A note on field-valued measures
- Topologies and uniformities on d0-algebras
- On some properties of 𝓙-approximately continuous functions
- Porous subsets in the space of functions having the Baire property
- Rademacher’s theorem in Banach spaces without RNP
- Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
- Measure games on pseudo-D-lattices
- On some properties of k-subadditive lattice group-valued capacities
- Lp Spaces in vector lattices and applications
- The Choquet integral with respect to fuzzy measures and applications
- A note on the range of vector measures
- Ideal convergent subsequences and rearrangements for divergent sequences of functions
- Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
- A generalization of the exponential sampling series and its approximation properties
- Monotonicity and total boundedness in spaces of “measurable” functions
- Vector lattices in synaptic algebras
- Density, ψ-density and continuity
- Feather topologies
- On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
- Rate of convergence of empirical measures for exchangeable sequences
- On non-additive probability measures
- Equi-topological entropy curves for skew tent maps in the square
- On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
