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New Banach spaces defined by the domain of Riesz-Fibonacci matrix

Pinar Zengin Alp|Emrah Evren Kara
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2021.12|한국수학논문집 (Korean Journal of Mathematics)|제29권 제4호|pp. 665-677

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참고문헌

키워드

Fibonacci numbersRiesz meansequence spacesmatrix operators
주제분류수학

초록

The main object of this study is to introduce the spaces $c_0(\widehat{F}^q)$ and $c(\widehat{F}^q)$ derived by the matrix $\widehat{F}^q$ which is the multiplication of Riesz matrix and Fibonacci matrix. Moreover, we find the $\alpha$-, $\beta$-, $\gamma$- duals of these spaces and give the characterization of matrix classes $(\Lambda(\widehat{F}^q),\Omega)$ and $(\Omega,\Lambda(\widehat{F}^q))$ for $\Lambda\in\{c_0,c\}$ and $\Omega\in\{\ell_1,c_0,c,\ell_\infty\}$.

Abstract

The main object of this study is to introduce the spaces $c_0(\widehat{F}^q)$ and $c(\widehat{F}^q)$ derived by the matrix $\widehat{F}^q$ which is the multiplication of Riesz matrix and Fibonacci matrix. Moreover, we find the $\alpha$-, $\beta$-, $\gamma$- duals of these spaces and give the characterization of matrix classes $(\Lambda(\widehat{F}^q),\Omega)$ and $(\Omega,\Lambda(\widehat{F}^q))$ for $\Lambda\in\{c_0,c\}$ and $\Omega\in\{\ell_1,c_0,c,\ell_\infty\}$.

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