Abstract:We introduce and study the Rhaly operator on Köthe spaces, with a primary focus on understanding its well-definedness, continuity, and compactness. We especially examine operators acting on power series spaces of both infinite and finite type. In the sequel, we provide integral representations for the Rhaly operator on the space of entire functions $H(\mathbb{C})$ and the space of holomorphic functions on the unit disc $H(\mathbb{D})$. We also investigate the topologizability and power boundedness of the Rhaly operators, which leads to findings about their mean ergodicity, uniform mean ergodicity, and Cesàro boundedness.
From: Nazlı Doğan [view email]
[v1]
Sun, 27 Jul 2025 10:40:25 UTC (31 KB)
[v2]
Mon, 18 Aug 2025 19:19:07 UTC (31 KB)
[v3]
Tue, 16 Jun 2026 12:02:05 UTC (30 KB)
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