Nearly invariant subspaces for shift semigroups

DOI10.1007/S11425-020-1915-YzbMATH Open1509.47066arXiv2012.11252MaRDI QIDQ6356594

Jonathan R. Partington, Yu-Xia Liang

Publication date: 21 December 2020

Abstract: Let ${T(t)}_{tgeq0}$ be a $C_0$-semigroup on an infinite dimensional separable Hilbert space; a suitable definition of near ${T(t{)}^{*}}_{tgeq0}$ invariance of a subspace is presented in this paper. A series of prototypical examples for minimal nearly ${S(t{)}^{*}}_{tgeq0}$ invariant subspaces for the shift semigroup ${S(t)}_{tgeq0}$ on $L^2(0,infty)$ are demonstrated, which have close links with nearly $T_{heta}^{*}$ invariance on Hardy spaces of the unit disk for Toeplitz operators associated with an inner function $heta$. 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.

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Invariant subspaces of linear operators (47A15) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

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