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http://dx.doi.org/10.5831/HMJ.2019.41.4.725

ORLICZ SEQUENCE SPACES OF FOUR DIMENSIONAL REGULAR MATRIX AND THEIR CLOSED IDEAL  

Raj, Kuldip (School of Mathematics, Shri Mata Vaishno Devi University)
Pandoh, Suruchi (School of Mathematics, Shri Mata Vaishno Devi University)
Choudhary, Anu (School of Mathematics, Shri Mata Vaishno Devi University)
Publication Information
Honam Mathematical Journal / v.41, no.4, 2019 , pp. 725-744 More about this Journal
Abstract
In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (artkl). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙2∞.
Keywords
Double sequence; Orlicz function; Paranorm space; Convergence of a double sequence and a double series; Regularity of four-dimensional infinite matrices; Silverman- Toeplitz theorem for double sequence and double series;
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