Erdal BAYRAM

On the Matrix Representations of Operators on the Classical Sequence Spaces

Sunulan çalışma, Banach örgüsü yapısına sahip bazı klasik dizi uzayları üzerinde tanımlı olan L-zayıf ve M-zayıf kompakt operatörlerin matris temsilleri için gerekli ve yeterli koşullar sağlar. Bu operatör sınıflarının, Banach örgüleri üzerinde tanımlı zayıf kompakt ve kompakt operatörlerle çakışabildiği bilinmektedir. Böylece kompakt ve zayıf kompakt operatörler için bilinen bazı sonuçlar L-zayıf ve M-zayıf kompaktlık açısından farklı bir alternatif olarak sunulmuş oldu.

Anahtar Kelimeler:

Matris dönüşümleri, Zayıf kompakt operatör, Kompakt operatör, L-zayıf kompakt operatör, M-zayıf kompakt operatör

On the Matrix Representations of Operators on the Classical Sequence Spaces

The present study provides the necessary and sufficient conditions for the matrix characterizations of ?- and ?-weakly compact operators which are defined on certain classical sequence spaces as Banach lattices. It is knownthat these operators may coincide with both weakly compact and compact operators on Banach lattices. Ourstudy offers a different alternative to some known results for the matrix characterizations of compact andweakly compact operators which are presented in terms of L- and M-weakly compactness.

Keywords:

Matrix transformation, Weakly compact operator, Compact operator, L-weakly compact operator, M-weakly compact operator,

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