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

Concrete Operators

Arcozzi Nicola¹  Levi Matteo¹ 

[1] University of Bologna, Bologna, Italy;

关键词: Drury-Arveson space;    Von Neumann’s inequality;    Hankel operators;    Invariant subspaces;    Reproducing kernel;    46E22;    47A15;    47A13;    47A20;    47A60;    47A63;   

DOI  :  10.1515/conop-2018-0001

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown