上三角算子矩阵的超环性和超环性

IF 0.9 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI:10.1007/s10114-025-3332-1

Gaohuizi Feng, Pengtong Li

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引用次数: 0

摘要

如果存在一个向量\(y \in \cal{H}\)，使得轨道Orb(T, y) = y, {Ty, T2y, T3y，…在}\(\cal{H}\)上是稠密的，则复可分无限维希尔伯特空间上的算子T是超循环的。对于2 × 2上三角算子矩阵，超循环性质和超循环性质容易失效。本文研究了2 × 2上三角算子矩阵的超环性和超环性。我们得到了2 × 2上三角算子矩阵的所有超循环算子类的范数闭包的谱表征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hypercyclicity and Supercyclicity for Upper Triangular Operator Matrices

An operator T on a complex separable infinite dimensional Hilbert space is hypercyclic if there is a vector \(y \in \cal{H}\) such that the orbit Orb(T, y) = {y, Ty, T²y, T³y, …} is dense in \(\cal{H}\). Hypercyclic property and supercyclic proeprty are liable to fail for 2 × 2 upper triangular operator matrices. In this paper, we aim to explore and characterize the hypercyclicity and the supercyclicity for 2 × 2 upper triangular operator matrices. We obtain a spectral characterization of the norm-closure of the class of all hypercyclic (supercyclic) operators for 2 × 2 upper triangular operator matrices.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.