WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Matrix Transforms Into the Set of a-absolutely Convergent Sequences with Speed and the Regularity of Matrices on the Sub-spaces of C
Authors: ,
Abstract: Let α > 1. The α-absolute convergence with speed, where the speed is defined by a monotonically increasing positive sequence μ, has been studied in the present paper. Let $$l^{μ}_{α}$$ be the set of all α-absolutely μ-convergent sequences and X a sequence space defined by another speed λ. Necessary and sufficient conditions for a matrix A (with real or complex entries) to map X into $$l^{μ}_{α}$$ have been presented. It is proved as an example that the Zweier matrix $$Z_{1/2}$$ satisfies these necessary and sufficient conditions for certain speeds λ and μ. The notion of regularity on the subspace X of the set c of converging sequences is defined, and also, necessary and sufficient conditions for a matrix A to be regular on certain X ⊂ c are presented. It has also been shown that there exists an irregular matrix, which is regular on the subspace X of c.
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Keywords: Matrix transforms, boundedness with speed, convergence with speed, α-absolute convergence with speed, Zweier matrix, regularity of matrices, regularity of a matrix on the subset of c.
Pages: 60-67
DOI: 10.37394/23206.2024.23.7