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

Abstract

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 g(M,Δ(m),v,p) $g(\mathcal{M},\Delta^{(m)}, v, p)$. 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
• Lorentz sequence space
• Garling sequence space
• Orlicz function
• Subsymmetric bases
• Symmetric bases