Quantized moment problem

Dosiev, Anar

doi:10.1016/j.crma.2007.03.022

Cited by 10 publications

(5 citation statements)

References 5 publications

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“…License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use Finally, confirm that some of the results of the present paper have been announced in [8].…”

Section: E (D) Ofsupporting

confidence: 77%

Local operator algebras, fractional positivity and the quantum moment problem

Dosi

2011

Trans. Amer. Math. Soc.

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Abstract. In the present paper we introduce quantum measures as a concept of quantum functional analysis and develop the fractional space technique in the quantum (or local operator) space framework. We prove that each local operator algebra (or quantum * -algebra) has a fractional space realization. This approach allows us to formulate and prove a noncommutative AlbrechtVasilescu extension theorem, which in turn solves the quantum moment problem.

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Section: E (D) Ofsupporting

confidence: 77%

Local operator algebras, fractional positivity and the quantum moment problem

Dosi

2011

Trans. Amer. Math. Soc.

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“…Some of the obtained results have been announced in [7] and they are applied to the quantized moment problems in [8].…”

Section: ϕ(A) ⊆ P H π(A) For All a ∈ Amentioning

confidence: 83%

“…The algebra C * E (D) can be treated as a quantized version of the (commutative) multinormed C * -algebra C(R n ) of all complex continuous functions on R n equipped with the compact-open topology (see [8]). Respectively, the space D can be referred as a quantized version of the locally compact space R n exhausted by an increasing family of compact subsets.…”

Section: Remark 32mentioning

confidence: 99%

Local operator spaces, unbounded operators and multinormed C*-algebras

Dosiev

2008

Journal of Functional Analysis

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In this paper we propose a representation theorem for local operator spaces which extends Ruan's representation theorem for operator spaces. Based upon this result, we introduce local operator systems which are locally convex versions of the operator systems and prove Stinespring theorem for local operator systems. A local operator C * -algebra is an example of a local operator system. Finally, we investigate the injectivity in both local operator space and local operator system senses, and prove locally convex version of the known result by Choi and Effros, that an injective local operator system possesses unique multinormed C * -algebra structure with respect to the original involution and matrix topology.

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“…By a quantum domain in a Hilbert space H we mean an upward filtered family E = {H α : α ∈ Λ} of its closed subspaces whose union space D = E is dense in H. Equivalently, a quantum domain is defined by means of an upward directed family of projections E = {p α : α ∈ Λ} in B (H) such that ∨ α p α = 1 H , where ∨ α p α is the least upper bound in B (H) of the projection net. The algebra of all noncommutative continuous functions on D is defined [5], [6], [7] as the O * -subalgebra…”

Section: Anar Dosimentioning

confidence: 99%

Multinormed $W^{∗}$-algebras and unbounded operators

Dosi

2012

Proc. Amer. Math. Soc.

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In this paper we investigate multinormed W *-algebras in terms of the central topologies of W *-algebras. The main result asserts that each multinormed W *-algebra can be realized as a local von Neumann algebra on a certain domain in a Hilbert space. Moreover, it admits the predual (unique up to an isometry), which is the 1-normed space. In the normed case the assertion is reduced to the known Sakai theorem.

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Quantized moment problem

Cited by 10 publications

References 5 publications

Local operator algebras, fractional positivity and the quantum moment problem

Local operator algebras, fractional positivity and the quantum moment problem

Local operator spaces, unbounded operators and multinormed C*-algebras

Multinormed $W^{∗}$-algebras and unbounded operators

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