scholarly journals The spectra of weighted mean operators on bν0

1992 ◽  
Vol 52 (2) ◽  
pp. 242-250 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Bounded Variation ◽  
Sequence Spaces ◽  
Bounded Operators ◽  
Weighted Mean ◽  
Weighted Mean Matrices ◽  
Weighted Mean Operators

AbstractIn a series of papers, the author has previously investigated the spectra and fine spectra for weighted mean matrices, considered as bounded operators over various sequence spaces. This paper examines the spectra of weighted mean matrices as operators over bνv0, the space of null sequences of bounded variation.

Simple Conditions for Matrices to be Bounded Operators on lp

1998 ◽  
Vol 41 (1) ◽  
pp. 10-14 ◽  
Author(s):  
David Borwein
Keyword(s):  
Bounded Operators ◽  
Weighted Mean ◽  
Triangular Matrices ◽  
Weighted Mean Matrices ◽  
General Conditions

AbstractThe two theorems proved yield simple yet reasonably general conditions for triangular matrices to be bounded operators on lp. The theorems are applied to Nörlund and weighted mean matrices.

scholarly journals On Domain of Nörlund Sequences

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 268 ◽  
Author(s):  
Kuddusi Kayaduman ◽  
Fevzi Yaşar
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Sequence Space ◽  
Convergent Series ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Nörlund Matrix ◽  
Inclusion Relations ◽  
The Matrix ◽  
New Space

In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space and and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α­, β­, γ­duals, and characterized their matrix transformations on this space and into this space.

Weighted Mean Operators on lp

2000 ◽  
Vol 43 (4) ◽  
pp. 406-412 ◽  
Author(s):  
David Borwein
Keyword(s):  
Triangular Matrix ◽  
Weighted Mean ◽  
Weighted Mean Operators

AbstractAbstract. The weightedmean matrix Ma is the triangular matrix {ak/An}, where an > 0 and An := a1 + a2 + … + an. It is proved that, subject to ncan being eventually monotonic for each constant c and to the existence of for 1 < p < ∞ if and only if α < p.

scholarly journals The Cesàro Operator on Some Sequence Spaces in Riesz Space of Non-Absolute Type

2020 ◽  
Vol 2 (2) ◽  
pp. 64-68
Author(s):  
E. Herawati ◽  
Supama
Keyword(s):  
Riesz Space ◽  
Sequence Spaces ◽  
Cesàro Operator ◽  
Bounded Operators ◽  
Cesaro Operator

The Cesàro operators are investigated on the class -valued sequence spaces , and with is a Riesz space. Besides, we also carry out that are order bounded operators.

scholarly journals On some spaces of summable sequences and their duals

1986 ◽  
Vol 9 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Geraldo Soares de Souza ◽  
G. O. Golightly
Keyword(s):  
Bounded Variation ◽  
Dual Space ◽  
Sequence Spaces ◽  
Simple Argument

Suppose thatSis the space of all summable sequencesαwith‖α‖S=supn≥0|∑j=n∞αj|andJthe space of all sequencesβof bounded variation with‖β‖J=|β0|+∑j=1∞|βj−βj−1|. Then forαinSandβinJ |∑j=0∞αjβj|≤‖α‖S‖β‖J; this inequality leads to the description of the dual space ofSasJ. It, related inequalities, and their consequences are the content of this paper. In particular, the inequality cited above leads directly to the Stolz form of Abel's theorem and provides a very simple argument. Also, some other sequence spaces are discussed.

scholarly journals Difference sequence spaces derived by using a generalized weighted mean

2011 ◽  
Vol 24 (5) ◽  
pp. 608-614 ◽  
Author(s):  
Harun Polat ◽  
Vatan Karakaya ◽  
Necip Şi̇mşek
Keyword(s):  
Sequence Spaces ◽  
Difference Sequence ◽  
Weighted Mean ◽  
Difference Sequence Spaces
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