On the Boundedness of a Recurrence Sequence in a Banach Space

• Date: 2003
• Main Authors: Gomilko, A. M., Gorodnii, M. F., Lagoda, O. A., Гомилко, А. М., Городний, М. Ф., Лагода, О. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2003
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4009
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate the problem of the boundedness of the following recurrence sequence in a Banach space B: \(x_n = \sum\limits_{k = 1}^\infty {A_k x_{n - k} + y_n } ,{ }n \geqslant 1,{ }x_n = {\alpha}_n ,{ }n \leqslant 0,\) where |y n} and |α n } are sequences bounded in B, and A k, k ≥ 1, are line...