A Survey on the Arveson-Douglas Conjecture

Guo, Kun; Wang, Yi

doi:10.1007/978-3-030-43380-2_13

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Cited by 4 publications

(2 citation statements)

References 54 publications

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“…I.t / ? is the solution operator to equation (21). We are especially interested in U WD U 2 2 B I.0/ ?…”

Section: Discussionmentioning

confidence: 99%

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Perturbations of principal submodules in the Drury–Arveson space

Jabbari

Tang

2023

J. Noncommut. Geom.

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“…I.t / ? is the solution operator to equation (21). We are especially interested in U WD U 2 2 B I.0/ ?…”

Section: Discussionmentioning

confidence: 99%

“…There have been many studies on Conjectures 1.1 and 1.2 in the last decades. A survey of results about these conjectures is given in [34,Chapter 41] and [21].…”

Section: Introductionmentioning

confidence: 99%

Perturbations of principal submodules in the Drury–Arveson space

Jabbari

Tang

2023

J. Noncommut. Geom.

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A Trace Inequality for Commuting d-Tuples of Operators

Misra

Pramanick

Sinha

2022

Integr. Equ. Oper. Theory

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In this semi-expository article, we investigate the relationship between the imprimitivity introduced by Mackey several decades ago and commuting d-tuples of homogeneous normal operators. The Hahn-Hellinger theorem gives a canonical decomposition of a * -algebra representation ρ of C 0 (S) (where S is a locally compact Hausdorff space) into a direct sum. If there is a group G acting transitively on S and is adapted to the * -representation ρ via a unitary representation U of the group G, in other words, if there is an imprimitivity, then the Hahn-Hellinger decomposition reduces to just one component, and the group representation U becomes an induced representation, which is Mackey's imprimitivity theorem. We consider the case where a compact topological space S ⊂ C d decomposes into finitely many G-orbits. In such cases, the imprimitivity based on S admits a decomposition as a direct sum of imprimitivities based on these orbits. This decomposition leads to a correspondence with homogeneous normal tuples whose joint spectrum is precisely the closure of G-orbits.

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The non-tangential boundary behavior of the matrix-valued rational inner functions on bounded symmetric domain

Wang

Zhang

2023

Proc. Amer. Math. Soc.

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Knese [Proc. LMS 111(2015), 1261-1306] proved every rational inner function on polydisc has a non-tangential limit at every point of the Shilov boundary. We extended his result to the case of functions on general bounded symmetric domains. Namely, every rational inner function on a bounded symmetric domain has a non-tangential limit of modulus 1 1 at every point of the Shilov boundary. We also prove that every matrix-valued rational inner function on tube-type domain has a unitary non-tangential limit at every point of the Shilov boundary.

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A Survey on the Arveson-Douglas Conjecture

Cited by 4 publications

References 54 publications

Perturbations of principal submodules in the Drury–Arveson space

Perturbations of principal submodules in the Drury–Arveson space

A Trace Inequality for Commuting d-Tuples of Operators

The non-tangential boundary behavior of the matrix-valued rational inner functions on bounded symmetric domain

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