Sequence Lorentz Spaces and Their Geometric Structure

Some p -Type New Sequence Spaces and Their Geometric Properties

and Applied Analysis 3 of the space λA is defined by λA {f : f g ◦ A; g ∈ λ′}. Let X be a seminormed space. A set Y ⊂ X is called fundamental set if the span of Y is dense in X. An application of HahnBanach theorem on fundamental set is as follows: if Y is the subset of a seminormed space X and f Y 0 implies f 0 for f ∈ X′, then Y is a fundamental set see 11 . By the idea mentioned above, let u...

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

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 sequen...

The Mackey Topology and Complemented Subspaces of Lorentz Sequence Spaces

In this paper we continue the study of Lorentz sequence spaces d(w,p), 0 < p < 1, initiated by N. Popa [8]. First we show that the Mackey completion of d(w,p) is equal to d(v, 1) for some sequence v. Next, we prove that if d(w, p) (2 h, then it contains a complemented subspace isomorphic to lp. Finally we show that if limn_1(X)"=1 wi)1 = °°, tnen every complemented subspace of d(w,p) with symme...

Some Geometric Properties of Sequence Spaces Involving Lacunary Sequence

NORMS OF CERTAIN OPERATORS ON WEIGHTED `p SPACES AND LORENTZ SEQUENCE SPACES

The problem addressed is the exact determination of the norms of the classical Hilbert, Copson and averaging operators on weighted `p spaces and the corresponding Lorentz sequence spaces d(w, p), with the power weighting sequence wn = n−α or the variant defined by w1 + · · ·+wn = n1−α. Exact values are found in each case except for the averaging operator with wn = n−α, for which estimates deriv...