Nearly invariant subspaces for shift semigroups

作     者：Yuxia Liang Jonathan R.Partington 

作者机构：School of Mathematical SciencesTianjin Normal UniversityTianjin 300387China School of MathematicsUniversity of LeedsLeeds LS 29JTUK 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2022年第65卷第9期

页      面：1895-1908页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11701422)。 

主　　题：nearly invariant subspace C_(0)-semigroup shift semigroup model space 

摘      要：Let{T(t)}_(t≥0) be a C_(0)-semigroupon 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 L^(2)(0,∞)are demonstrated,which have close links with near T_(θ)^(*)invariance on Hardy spaces of the unit disk for an inner functionθ.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.