On factor states of 𝐶*-algebras and their extensions

Chu, Cho-Ho; Kusuda, Masaharu

doi:10.1090/s0002-9939-96-03026-2

Cited by 3 publications

(1 citation statement)

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“…On the other hand, there is a class of type-I C ¤ -algebras called dual, which have often appeared recently (see, for example, [2,3,6]), although it has been a long time since the notion of a dual C ¤ -algebra was rst introduced by Kaplansky [5] (see also [4, 4.7.20]). Recall that a C ¤ -algebra A is said to be dual if the sum of the minimal left ideals of A is dense in A, or, equivalently, A is isomorphic to a C ¤ -subalgebra of the C ¤ -algebra of all compact operators on some Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

Three-space problems in discrete spectra of C-algebras and dual C-algebras

Kusuda¹

2001

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Section: Introductionmentioning

confidence: 99%

Three-space problems in discrete spectra of C-algebras and dual C-algebras

Kusuda¹

2001

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Extensions of Pure States and Projections of Norm One

Archbold¹

1999

Journal of Functional Analysis

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We show that the extension property for pure states of a C*-subalgebra B of a C*-algebra A leads to the existence of a projection of norm one R: A Ä B in the case where B is liminal with Hausdorff primitive ideal space. Furthermore, R is given by a``Dixmier process'' in which the averaging is effected by a group of unitary elements in the centre of the multiplier algebra M(B). These results generalize earlier work of J. Anderson and the author for the case when B is a masa of A. Various applications are given in the context of inductive limit algebras such as AF algebras and, more generally, Kumjian's ultraliminary C*-algebras. Academic Press

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On weak sequential convergence in JB^*-triple duals

Bunce

Peralta

2004

Studia Math.

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Abstract. We study various Banach space properties of the dual space E * of a homogeneous Banach space (alias, a JB * -triple) E. For example, if all primitive M -ideals of E are maximal, we show that E * has the Alternative Dunford-Pettis property (respectively, the Kadec-Klee property) if and only if all biholomorphic automorphisms of the open unit ball of E are sequentially weakly continuous (respectively, weakly continuous). Those E for which E * has the weak * Kadec-Klee property are characterised by a compactness condition on E. Whenever it exists, the predual of E is shown to have the Kadec-Klee property if and only if E is atomic with no infinite spin part.

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On factor states of 𝐶*-algebras and their extensions

Abstract: Abstract. We obtain some results on the unique extension of (factor) states of C * -algebras which complement various existing results. Our results also lead to a class of C * -algebras whose states are σ-convex sums of factor states.

Cited by 3 publications

References 25 publications

Three-space problems in discrete spectra of C-algebras and dual C-algebras

Three-space problems in discrete spectra of C-algebras and dual C-algebras

Extensions of Pure States and Projections of Norm One

On weak sequential convergence in JB^*-triple duals

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On factor states of 𝐶*-algebras and their extensions

Abstract: Abstract. We obtain some results on the unique extension of (factor) states of C * -algebras which complement various existing results. Our results also lead to a class of C * -algebras whose states are σ-convex sums of factor states.

Cited by 3 publications

References 25 publications

Three-space problems in discrete spectra of C*-algebras and dual C*-algebras

Three-space problems in discrete spectra of C*-algebras and dual C*-algebras

Extensions of Pure States and Projections of Norm One

On weak sequential convergence in JB*-triple duals

Contact Info

Product

Resources

About

Three-space problems in discrete spectra of C-algebras and dual C-algebras

Three-space problems in discrete spectra of C-algebras and dual C-algebras

On weak sequential convergence in JB^*-triple duals