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The Joly–Becker theorem for * –orderings

Igor Klep, Dejan Velušček (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the * –version of the Joly–Becker theorem: a skew field admits a * –ordering of level n iff it admits a * –ordering of level n ℓ for some (resp. all) odd ℓ ∈ ℕ . For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a * –ordering of higher level also admits a * –ordering of level 1 . Every field that admits a * –ordering of higher level admits a * –ordering of level 1 or 2

The Kadison problem on a class of commutative Banach algebras with closed cone

M. A. Toumi (2010)

Commentationes Mathematicae Universitatis Carolinae

The main result of the paper characterizes continuous local derivations on a class of commutative Banach algebra A that all of its squares are positive and satisfying the following property: Every continuous bilinear map Φ from A × A into an arbitrary Banach space B such that Φ ( a , b ) = 0 whenever a b = 0 , satisfies the condition Φ ( a b , c ) = Φ ( a , b c ) for all a , b , c ∈ A .

The nil radical of an Archimedean partially ordered ring with positive squares

Boris Lavrič (1994)

Commentationes Mathematicae Universitatis Carolinae

Let R be an Archimedean partially ordered ring in which the square of every element is positive, and N ( R ) the set of all nilpotent elements of R . It is shown that N ( R ) is the unique nil radical of R , and that N ( R ) is locally nilpotent and even nilpotent with exponent at most 3 when R is 2-torsion-free. R is without non-zero nilpotents if and only if it is 2-torsion-free and has zero annihilator. The results are applied on partially ordered rings in which every element a is expressed as a = a 1 - a 2 with positive a 1 ,...

The order topology for a von Neumann algebra

Emmanuel Chetcuti, Jan Hamhalter, Hans Weber (2015)

Studia Mathematica

The order topology τ o ( P ) (resp. the sequential order topology τ o s ( P ) ) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part M s a , the self-adjoint part of the unit ball M ¹ s a , and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology to the other...

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