Reducing subspaces of de Branges-Rovnyak spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:477

Article

Chu, Cheng¹ 

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

关键词: Reducing subspace;    de Branges-Rovnyak space;    Backward shift operator;   

DOI  :  10.1016/j.jmaa.2019.04.071

来源: Elsevier

【 摘 要 】

For b is an element of H-1(infinity), the closed unit ball of H-infinity, the de Branges-Rovnyak space H(b) is a Hilbert space contractively contained in the Hardy space H-2 that is invariant by the backward shift operator S*. We consider the reducing subspaces of the operator S*(2)vertical bar(H(b)). When b is an inner function, S*(2)vertical bar(H(b)) is a truncated Toeplitz operator and its reducibility was characterized by Douglas and Foias using model theory. We use another approach to extend their result to the case where b is extreme. We prove that if b is extreme but not inner, then S*(2)vertical bar(H(b)) is reducible if and only if b is even or odd, and describe the structure of reducing subspaces. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free