Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Foulis David J."'
Autor:
Foulis David J., Pulmannová Sylvia
Publikováno v:
Demonstratio Mathematica, Vol 51, Iss 1, Pp 1-7 (2018)
We prove that if A is a synaptic algebra and the orthomodular lattice P of projections in A is complete, then A is a factor if and only if A is an antilattice.We also generalize several other results of R. Kadison pertaining to infima and suprema in
Externí odkaz:
https://doaj.org/article/61285e7b1e634ecbb87a85dbe7813300
Autor:
Foulis, David J., Pulmannova, Sylvia
We define and study an alternative partial order, called the spectral order, on a synaptic algebra-a generalization of the self-adjoint part of a von Neumann algebra. We prove that if the synaptic algebra A is norm complete (a Banach synaptic algebra
Externí odkaz:
http://arxiv.org/abs/1709.03801
Autor:
Foulis, David J., Pulmannova, Sylvia
We prove that if A is a synaptic algebra and the orthomodular lattice P of projections in A is complete, then A is a factor iff A is an antilattice. We also generalize several other results of R. Kadison pertaining to infima and suprema in operator a
Externí odkaz:
http://arxiv.org/abs/1706.01719
Autor:
Foulis, David J., Pulmannova, Sylvia
Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Stormer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C*-alg
Externí odkaz:
http://arxiv.org/abs/1705.01011
A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tribe, which is a commutative GH-algebra of functions on a nonempty set $
Externí odkaz:
http://arxiv.org/abs/1610.06208
Autor:
Foulis, David J., Pulmannová, Sylvia
We give a detailed proof D. Handelman's theorem stating (in the context of an order unit normed space) that a monotone sigma-complete order unit normed space is a Banach space.
Externí odkaz:
http://arxiv.org/abs/1609.08014
Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic algebras and on its sub-structures. A synaptic algebra is a generalization
Externí odkaz:
http://arxiv.org/abs/1606.08229
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 e
Externí odkaz:
http://arxiv.org/abs/1605.06987
A synaptic algebra is a common generalization of several ordered algebraic structures based on algebras of self-adjoint operators, including the self-adjoint part of an AW*-algebra. In this paper we prove that a synaptic algebra A has the monotone sq
Externí odkaz:
http://arxiv.org/abs/1605.04115
Publikováno v:
Lin. Alg. Appl. 485 (2015) 417-441
We study a pair p,e consisting of a projection p (an idempotent) and an effect e (an element between 0 and 1) in a synaptic algebra (a generalization of the self-adjoint part of a von Neumann algebra). We show that some of Halmos's theory of two proj
Externí odkaz:
http://arxiv.org/abs/1507.08965