On the Kr-Core of Complex Sequences and the Absolute Equivalence of Summability Matrices

Celal Çakan; Cafer Aydin

doi:10.3390/mca9030409

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Article

1 December 2004

On the Kr-Core of Complex Sequences and the Absolute Equivalence of Summability Matrices

and

İnönü Üniversitesi Eğitim Fakültesi, 44069-Malatya, Turkey

Kahramanmaraş Sütçü İmam Üniversitesi, Fen-Edeblyat Fakültesi, Kahramanmaraş, Turkey

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Math. Comput. Appl.2004, 9(3), 409-416;https://doi.org/10.3390/mca9030409

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Abstract

The K_r-core of a complex valued sequence has been introduced in [5]. In this paper, we have determined a class of matrices such that K_r - core (Ax) ⊆ K_r - core (x) hold for all x ∈ L_∞. Also; we have defined a new type of absolute equivalence, r - absolute equivalence, and characterized these type of matrices.

Keywords:

Sequence spaces; absolute equivalence; matrix transformations; core theorems

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