MUTLAK EULER TOTİENT SERİ UZAYI VE BAZI MATRİS DÖNÜŞÜMLERİ ÜZERİNE BİR ÇALIŞMA

Son zamanlarda birçok yazar dizi ve seri uzayları ile ilgili çalışmalara yoğunlaşmışlardır. Literatürde basit ve temel yaklaşım klasik dizi uzayları üzerinde üçgensel matrislerin matris etki alanı yardımıyla yeni dizi ve seri uzayları inşa etmektir. Bu çalışmada, bu yaklaşımdan yola çıkarak ?, ?? ? mutlak toplanabilme metodu ile toplanabilen tüm serilerin uzayı olan yeni bir ?? ? seri uzayı tanımlanmıştır, burada ? = ??? Euler totient matrisini gösterir, ? = ?? terimleri negatif olmayan bir dizidir ve ? ≥ 1 dir. ?? ? seri uzayının tüm mutlak ?- toplanabilen dizilerin ℓ? , ? ≥ 1, uzayına izomorf olduğu gösterilmiştir. Ayrıca, bu uzayın bazı topolojik özellikleri ile ?, ? and ?- dualleri belirlenmiştir ve ?? ? uzayı için Schauder bazı verilmiştir. Son olarak, |?? |? uzayından ℓ∞ , ?, ?0, ℓ1 klasik dizi uzaylarına ve ℓ∞ , ?, ?0, ℓ1 klasik dizi uzaylarından |?? |? uzayına bazı matris operatörleri karakterize edilmiştir.

A STUDY ON ABSOLUTE EULER TOTIENT SERIES SPACE AND CERTAIN MATRIX TRANSFORMATIONS

Recently, many authors have focused on the studies related to sequence and series spaces. In the literature the simple andfundamental method is to construct new sequence and series spaces by means of the matrix domain of triangularmatrices on the classical sequence spaces. Based on this approach, in this study, we introduce a new series space ?? ? asthe set of all series summable by absolute summability method ?, ?? ? , where ? = ??? denotes Euler totient matrix,? = ?? is a sequence of non-negative terms and ? ≥ 1. Also, we show that the series space ?? ? is linearly isomorphicto the space of all ?- absolutely summable sequences ℓ? for ? ≥ 1. Moreover, we determine some topological propertiesand ?, ? and ?-duals of this space and give Schauder basis for the space ?? ? . Finally, we characterize the classes of thematrix operators from the space |?? |? to the classical spaces ℓ∞ , ?, ?0, ℓ1 for 1 ≤ ? < ∞ and vice versa.

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