A Characterization of the Dual of the Classical Lorentz Sequence Space d(w, q)

1991 ◽  
Vol 112 (1) ◽  
pp. 87 ◽  
Author(s):  
Miguel A. Arino ◽  
Benjamin Muckenhoupt
Keyword(s):  
Sequence Space ◽  
Lorentz Sequence Space

Some criteria for nuclearity

1986 ◽  
Vol 100 (1) ◽  
pp. 151-159 ◽  
Author(s):  
M. A. Sofi
Keyword(s):  
Sequence Space ◽  
Convex Space ◽  
Locally Convex Space ◽  
Sequence Spaces ◽  
Bilinear Forms ◽  
Simple Formulation ◽  
Normal Topology ◽  
Nuclear Spaces ◽  
Locally Convex

For a given locally convex space, it is always of interest to find conditions for its nuclearity. Well known results of this kind – by now already familiar – involve the use of tensor products, diametral dimension, bilinear forms, generalized sequence spaces and a host of other devices for the characterization of nuclear spaces (see [9]). However, it turns out, these nuclearity criteria are amenable to a particularly simple formulation in the setting of certain sequence spaces; an elegant example is provided by the so-called Grothendieck–Pietsch (GP, for short) criterion for nuclearity of a sequence space (in its normal topology) in terms of the summability of certain numerical sequences.

scholarly journals The weak cotype 2 and the Orlicz property of the Lorentz sequence space d(a, 1)

1992 ◽  
Vol 34 (3) ◽  
pp. 271-276
Author(s):  
J. Zhu
Keyword(s):  
Banach Space ◽  
Function Space ◽  
Sequence Space ◽  
Affirmative Answer ◽  
Sequence Spaces ◽  
Similar Question ◽  
Lorentz Sequence Space ◽  
Symmetric Basis ◽  
Orlicz Property

The question “Does a Banach space with a symmetric basis and weak cotype 2 (or Orlicz) property have cotype 2?” is being seriously considered but is still open though the similar question for the r.i. function space on [0, 1] has an affirmative answer. (If X is a r.i. function space on [0, 1] and has weak cotype 2 (or Orlicz) property then it must have cotype 2.) In this note we prove that for Lorentz sequence spaces d(a, 1) they both hold.

scholarly journals On boundaries on the predual of the Lorentz sequence space

2007 ◽  
Vol 336 (1) ◽  
pp. 470-479 ◽  
Author(s):  
María D. Acosta ◽  
Luiza A. Moraes ◽  
Luis Romero Grados
Keyword(s):  
Sequence Space ◽  
Lorentz Sequence Space

scholarly journals On generalized Lorentz sequence space defined by modulus functions

Filomat ◽  
2016 ◽  
Vol 30 (2) ◽  
pp. 497-504 ◽  
Author(s):  
Oğuz Oğur ◽  
Cenap Duyar
Keyword(s):  
Sequence Space ◽  
Lorentz Sequence Space

On the space of p -summable difference sequences of order m , (1 ≦ p < ∞)

2006 ◽  
Vol 43 (4) ◽  
pp. 387-402 ◽  
Author(s):  
Bilâl Altay
Keyword(s):  
Sequence Space ◽  
Difference Sequence ◽  
Order Difference ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
The Matrix ◽  
The Difference ◽  
Matrix Mappings ◽  
Difference Sequence Spaces

The difference sequence spaces ℓ ∞ (Δ), c (Δ) and c0 (Δ) were studied by  Kizmaz [8]. The difference sequence space bvp , generated from the space ℓ p , has recently been introduced by Başar and Altay [5]. Several papers deal with the sets of sequences whose mth order difference are bounded, convergent or convergent to zero. The main purpose of the present paper is to introduce the space ℓ p (Δ (m) ) consisting of all sequences whose mth order differences are p -absolutely summable, and is to fill up the gap in the existing literature. Moreover, we give some topological properties and inclusion relations, a Schauder basis and determine the α-, β-, γ- and f- duals of the space ℓ p (Δ (m) ). The last section of the paper has been devoted to the characterization of the matrix mappings on the sequence space ℓ p (Δ (m) ).

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