Typicality of operators on Fréchet algebras admitting a hypercyclic algebra

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-06-18 DOI:10.1016/j.aim.2025.110406

William Alexandre , Clifford Gilmore , Sophie Grivaux

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引用次数: 0

Abstract

This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fréchet algebras, endowed with the topology of pointwise convergence. Our main results show that within natural Polish spaces of continuous operators acting on the algebra

H (C)

of entire functions on

C

, a typical operator supports a hypercyclic algebra. We also investigate the case of the complex Fréchet algebras

X = ℓ_{p} (N)

1 \leq p < + \infty

, or

X = c_{0} (N)

endowed with the coordinatewise product, and show that whenever

M > 1

, a typical operator on X of norm less than or equal to M admits a hypercyclic algebra.

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具有超循环代数的fr代数上算子的典型性

本文研究了具有点向收敛拓扑的fr代数上的连续线性算子的典型性质（在Baire范畴意义上）。我们的主要结果表明，在作用于C上的整个函数的代数H(C)的连续算子的自然波兰空间内，一个典型算子支持一个超循环代数。我们还研究了具有坐标积的复fr代数X= p(N), 1≤p<+∞，或X=c0(N)的情况，并证明了当M>；1时，一个范数小于或等于M的X上的典型算子存在一个超循环代数。

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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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.