The Second Dual Spaces of the Sets of Λ-strongly Convergent and Bounded Sequences
نویسنده
چکیده
We give the second β-, γ-, and f -duals of the sets w 0 (Λ), w p ∞(Λ) (0<p <∞), c 0 (Λ), c p(Λ), and c ∞(Λ) (0 < p ≤ 1) and the second continuous dual spaces of w 0 (Λ), c 0 (Λ), and c p(Λ) for 0< p ≤ 1. Furthermore, we determine the α-duals of c 0 (Λ), cp(Λ), and c ∞(Λ) for 1<p <∞.
منابع مشابه
On the Spaces of $lambda _{r}$-almost Convergent and $lambda _{r}$-almost Bounded Sequences
The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...
متن کاملSome Sequence Spaces and Statistical Convergence
for sets of sequences x = (xk) which are strongly (V ,λ)-summable to L, that is, xk → L[V,λ]. We recall that a modulus f is a function from [0,∞) to [0,∞) such that (i) f(x)= 0 if and only if x = 0; (ii) f(x+y)≤ f(x)+f(y) for all x, y ≥ 0; (iii) f is increasing; (iv) f is continuous from the right at 0. It follows that f must be continuous on [0,∞). A modulus may be bounded or unbounded. Maddox...
متن کاملB. de Malafosse ON THE SETS OF SEQUENCES THAT ARE STRONGLY α−BOUNDED AND α−CONVERGENT TO NAUGHT WITH INDEX p
In this paper we deal with sets of sequences generalizing the well known spaces w p ∞ (λ) = { X/C (λ) ( |X |p ) ∈ l∞ } and c∞ (λ) = (w∞ (λ))1(λ). We consider the set ( w p α (λ) ) 1(μ) and the cases when the operators C (λ) and 1(μ) are replaced by their transposes. These results generalize in a certain sense those given in [4, 10, 11, 13, 14, 16]. 1. Notations and preliminary results. For a gi...
متن کاملStrongly almost ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function
In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.
متن کاملOn Interval Valued Generalized Difference Classes Defined by Orlicz Function
The work of interval arithmetic was originally introduced by Dwyer [3] in 1951. The development of interval arithmetic as a formal system and evidence of its value as a computational device was provided by Moore [15] and Moore and Yang [16]. Furthermore, Moore and others [3]; [4]; [10] and [17] have developed applications to differential equations. Chiao in [2] introduced sequence of interval n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000