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2017 One dimensional perturbation of invariant subspaces in the Hardy space over the bidisk II
Kei Ji Izuchi, Kou Hei Izuchi, Yuko Izuchi
Nihonkai Math. J. 28(1): 31-42 (2017).

Abstract

This paper is a continuation of the previous paper [9]. Let $M_1$ be an invariant subspace of $H^2$ over the bidisk. Then there exists a nonzero $f_0$ in $M_1$ such that $M_2:=M_1\ominus \mathbb{C} \cdot f_0$ is also an invariant subspace. A relationship is given the ranks of the cross commutators $[R^*_z,R_w]$ on $M_1$ and $M_2$. We also give a relationship of the ranks of the cross commutators $[S_w,S^*_z]$ on $H^2\ominus M_1$ and $H^2\ominus M_2$.

Funding Statement

The first author is supported by JSPS KAKENHI Grant Number 15K04895.

Citation

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Kei Ji Izuchi. Kou Hei Izuchi. Yuko Izuchi. "One dimensional perturbation of invariant subspaces in the Hardy space over the bidisk II." Nihonkai Math. J. 28 (1) 31 - 42, 2017.

Information

Received: 24 December 2015; Revised: 11 May 2016; Published: 2017
First available in Project Euclid: 7 March 2018

zbMATH: 06714331
MathSciNet: MR3771366

Subjects:
Primary: 32A35‎, 47A15
Secondary: 47B35

Rights: Copyright © 2017 Niigata University, Department of Mathematics

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Vol.28 • No. 1 • 2017
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