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Supporting sequences of pure states on JB algebras

100%

Hamhalter J.

Studia Mathematica

1999

tom 136

nr 1

37-47

We show that any sequence $(φ_n)$ of mutually orthogonal pure states on a JB algebra A such that $(φ_n)$ forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence $(a_n)$ consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for $(φ_n)$ in the sense of $φ_n(a_n)=1$ for all n. Moreover, if A is separable then $(a_n)$ can be taken such that $(φ_n)$ is uniquely determined by the biorthogonality condition $φ_n(a_n)=1$. Consequences of this result improving hitherto known extension theorems for C*-algebras and descriptions of dual JB algebras are given.

The order topology for a von Neumann algebra

51%

Chetcuti E., Hamhalter J., Weber H.

Studia Mathematica

2015

tom 230

nr 2

95-120

The order topology $τ_{o}(P)$ (resp. the sequential order topology $τ_{os}(P)$) 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 $M_{sa}$, the self-adjoint part of the unit ball $M¹_{sa}$, 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 standard locally convex topologies on M, and relate the properties of the order topology to the underlying operator-algebraic structure of M.

Ograniczanie wyników

2 Studia Mathematica

2 Hamhalter J.

1 Chetcuti E.

1 Weber H.

1 2015

1 1999

Wyniki wyszukiwania

Supporting sequences of pure states on JB algebras

The order topology for a von Neumann algebra