On Some New BK-Spaces as the Domain of (p,q)-Cesàro Matrix and Point Spectrum

Iranian Journal of Science - Tập 47 - Trang 1565-1574 - 2023
Taja Yaying1, Bipan Hazarika2, Mohammad Mursaleen3,4
1Department of Mathematics, Dera Natung Government College, Itanagar, India
2Department of Mathematics, Gauhati University, Gauhati, India
3Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan
4Department of Mathematics, Aligarh Muslim University, Aligarh, India

Tóm tắt

We study new BK-spaces $$X^{p,q}_c$$ and $$X^{p,q}_0$$ as the domain of (p, q)-Cesàro matrix $$C^{p, q}$$ in the spaces c and $$c_0$$ , respectively. We study certain topological properties and inclusion relations, and obtain Schauder basis and Alpha-, Beta- and Gamma-duals of the spaces $$X^{p,q}_c$$ and $$X^{p,q}_0$$ . Further, we determine necessary and sufficient conditions for a matrix operator to map from the spaces $$X^{p,q}_c$$ and $$X^{p,q}_0$$ to the space $$\mu \in \{\ell _{\infty },c,c_0,\ell _{1},\ell _s\}$$ . Finally, we determine the point spectrum of $$C^{p, q}$$ operator over the space $$c_0$$ .

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