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

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
• 46E22
• 47A15
• 47A13
• 47A20
• 47A60
• 47A63