On the Matrix Representations of Operators on the Classical Sequence Spaces

Year 2019, Volume: 12 Issue: 1, 489 - 498, 24.03.2019

Erdal Bayram

https://doi.org/10.18185/erzifbed.508746

Abstract

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.

Keywords

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

Abstract

The present study provides the necessary and sufficient conditions for the matrix characterizations of 𝐿- and 𝑀-

weakly compact operators which are defined on certain classical sequence spaces as Banach lattices. It is known

that these operators may coincide with both weakly compact and compact operators on Banach lattices. Our

study offers a different alternative to some known results for the matrix characterizations of compact and

weakly 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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