On Pell Sequence Spaces - Atabey, Koray Ibrahim; Kalita, Hemanta; Et, Mikail (Palestine Polytechnic University, 2025)
In this article, we introduce the recurrence relation of the sequence Sn obtained by the sum of the Pell numbers, and that the sequence of ratios of two consecutive Sn terms is equal to the silver ratio. We construct a new triangular analogue of the Pell matrix (Formula Presented) defined by (Formula Presented) Further, we introduce sequence spaces (Formula Presented). Moreover, some inclusion relations for these spaces and examine a few topological characteristics. Furthermore, we construct a basis for the space (Formula Presented)?duals of the same space, characterize certain matrix classes, and look at some geometric properties. © Palestine Polytechnic University-PPU 2025.
Keywords: Banach-Saks Property; Dual Spaces; Matrix Transform; Pell Numbers