Nearly invariant subspaces for shift semigroups

2020/12/21 by Liang, Yuxia, Partington, Jonathan R. · 2 citations
#43A15 #47A15 #47B38 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2012.11252

Abstract

Let \T(t)\_t≥0 be a C₀-semigroup on an infinite dimensional separable Hilbert space; a suitable definition of near \T(t)^*\_t≥0 invariance of a subspace is presented in this paper. A series of prototypical examples for minimal nearly \S(t)^*\_t≥0 invariant subspaces for the shift semigroup \S(t)\_t≥0 on L²(0,∞) are demonstrated, which have close links with nearly T_θ^* invariance on Hardy spaces of the unit disk for Toeplitz operators associated with an inner function θ. Especially, the corresponding subspaces on Hardy spaces of the right half-plane and the unit disk are related to model spaces. This work further includes a discussion on the structure of the closure of certain subspaces related to model spaces in Hardy spaces.

Cited by

• Perturbations of Toeplitz operators on vector-valued Hardy spaces
• Spectra and invariant subspaces of compressed shifts on nearly invariant subspaces

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