Spectra and dynamics of generalized Cesàro operators in (LF) and (PLB) sequence spaces

被引：0

作者：

Albanese, Angela A. ^{[1
]}

Asensio, Vicente ^{[2
,3
]}

机构：

[1] Univ Salento, Dipartimento Matemat & Fis E di Giorgi, CP 193, I-73100 Lecce, Italy

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada IUMPA, Camino Vera S-N, Valencia 46022, Spain

[3] Ctr Univ EDEM, Placa Aigua S-N, Valencia 46024, Spain

来源：

POSITIVITY | 2024年 / 28卷 / 03期

关键词：

Generalized Ces & agrave; ro operator; Spectrum; Power boundedness; Uniform mean ergodicity; Supercyclicity; Sequence spaces; (LF)-space; (PLB)-space; DUAL BANACH-SPACES; CESARO OPERATOR; FINE SPECTRUM; FRECHET; CES(P+);

D O I：

10.1007/s11117-024-01060-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce inductive limits of the Fr & eacute;chet spaces l (p+), ces(p+),andd(p+)(1 <= p<infinity) and projective limits of the (LB)-spaces l(p-), ces(p-),andd(p-)(1<p <=infinity). After having established some topological properties ofsuch spaces as acyclicity and ultrabornologicity, we prove that the generalized Ces & agrave;rooperatorsC(t)(0 <= t <= 1) act continuously in these sequence spaces, and we determinethe spectra. Finally, we study the ergodic properties, that is, power boundedness,(uniform) mean ergodicity, and supercyclicity, of the operatorsCtacting in the (LF)-spaces and in the (PLB)-spaces mentioned above

引用

页数：26

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