Reducing Subspaces of the Dual Truncated Toeplitz Operator

Yinyin Hu,Liu Liu,Jia Deng,Tao Yu,Yufeng Lu

doi:10.1155/2018/7058401

Abstract

We define the dual truncated Toeplitz operators and give some basic properties of them. In particular, spectrum and reducing subspaces of some special dual truncated Toeplitz operator are characterized.

Highlights

Let D denote the open unit disk in the complex plane C and T denote the unit circle
For φ ∈ L∞, the Toeplitz operator Tφ on H2, with symbol φ, is defined by
Kang and Kim [24] characterized the pairs of truncated Hankel operator on the model spaces Ku2 whose products result in truncated Toeplitz operators when the inner function u has a certain symmetric property

Summary

Introduction

Let D denote the open unit disk in the complex plane C and T denote the unit circle. As usual, L2 denotes the Hilbert space of Lebesgue square integral functions on T with the inner product:. For φ ∈ L2, the truncated Toeplitz operator Aφ with symbol φ is defined by. Gu [23] defined truncated Hankel operator (THO) as the compression of Hankel operator to invariant subspaces for the backward shift and proved a number of algebraic properties of them. Kang and Kim [24] characterized the pairs of truncated Hankel operator on the model spaces Ku2 whose products result in truncated Toeplitz operators when the inner function u has a certain symmetric property. We will define dual truncated Toeplitz operators and introduce some algebraic properties of them. Let φ ∈ L∞, and the dual truncated Toeplitz operator Bφ on Ku2⊥ with symbol φ is defined by.

Basic Properties

Spectrum and Reducing Subspace