Skip to content
BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access April 28, 2018

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

  • Nicola Arcozzi EMAIL logo and Matteo Levi
From the journal Concrete Operators


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.

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


[1] William Arveson. Subalgebras of C.-algebras. III. Multivariable operator theory. Acta Math., 181(2):159-228, 1998.10.1007/BF02392585Search in Google Scholar

[2] Joseph A. Ball, Tavan T. Trent, and Victor Vinnikov. Interpolation and Commutant Lifting for Multipliers on Reproducing Kernel Hilbert Spaces, pages 89-138. Birkhäuser Basel, Basel, 2001.10.1007/978-3-0348-8283-5_4Search in Google Scholar

[3] S. W. Drury. A generalization of von Neumann’s inequality to the complex ball. Proc. Amer. Math. Soc., 68(3):300-304, 1978.10.1090/S0002-9939-1978-0480362-8Search in Google Scholar

[4] Vladimir V Peller. An excursion into the theory Hankel operators. Holomorphic spaces (Berkeley, CA, 1995), Math. Sci. Res. Inst. Publ, 33:65-120, 1998.Search in Google Scholar

[5] Stefan Richter and James Sunkes. Hankel operators, invariant subspaces, and cyclic vectors in the Drury-Arveson space. Proc. Amer. Math. Soc., 144, 2016.10.1090/proc/12922Search in Google Scholar

[6] Donald Sarason. Generalized interpolation in Hª. Transactions of the American Mathematical Society, 127(2):179-203, 1967.10.1090/S0002-9947-1967-0208383-8Search in Google Scholar

[7] Orr Shalit. Operator theory and function theory in Drury-Arveson space and its quotients. Operator Theory, pages 1125- 1180, 2015.10.1007/978-3-0348-0667-1_60Search in Google Scholar

[8] James Allen Sunkes III. Hankel operators on the Drury-Arveson space. PhD diss., University of Tennessee, 2016.Search in Google Scholar

[9] Béla Sz.-Nagy and Ciprian Foias. Harmonic analysis of operators on Hilbert space. Translated from the French and revised. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970.Search in Google Scholar

Received: 2017-03-11
Accepted: 2018-02-09
Published Online: 2018-04-28

© 2018, published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Downloaded on 26.3.2023 from
Scroll Up Arrow