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Concrete Operators

Ed. by Chalendar, Isabelle / Partington, Jonathan

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Mathematical Citation Quotient (MCQ) 2016: 0.38


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On a class of shift-invariant subspaces of the Drury-Arveson space

Nicola Arcozzi / Matteo Levi
Published Online: 2018-04-28 | DOI: https://doi.org/10.1515/conop-2018-0001

Abstract

In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in a set Y⊂ ℕd with the property that ℕ\X + ej ⊂ ℕ\X for all j = 1, . . . , d. This is an easy example of shift-invariant subspace, which can be considered as a RKHS in is own right, with a kernel that can be explicitly calculated for specific choices of X. Every such a space can be seen as an intersection of kernels of Hankel operators with explicit symbols. Finally, this is the right space on which Drury’s inequality can be optimally adapted to a sub-family of the commuting and contractive operators originally considered by Drury.

Keywords: Drury-Arveson space; Von Neumann’s inequality; Hankel operators; Invariant subspaces; Reproducing kernel

MSC 2010: 46E22; 47A15; 47A13; 47A20; 47A60; 47A63

References

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About the article

Received: 2017-03-11

Accepted: 2018-02-09

Published Online: 2018-04-28


Citation Information: Concrete Operators, Volume 5, Issue 1, Pages 1–8, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2018-0001.

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© 2018. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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