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J Inequal Appl. 2018;2018(1):34. doi: 10.1186/s13660-018-1621-2. Epub 2018 Feb 7.

Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces.

Author information

1
1School of Mathematics, Shri Mata Vaishno Devi University, Katra, India.
2
2Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
3
3Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia.

Abstract

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text]. We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequence dominates an Orlicz-Lorentz sequence. Finally, we study some geometric properties of these spaces and establish some inclusion relations between spaces.

KEYWORDS:

Banach space; Garling sequence space; Lorentz sequence space; Orlicz function; Subsymmetric bases; Symmetric bases

Conflict of interest statement

The authors declare that they have no competing interests.

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