Simple Conditions for Matrices to be Bounded Operators on lp

1998 ◽  
Vol 41 (1) ◽  
pp. 10-14 ◽  
Author(s):  
David Borwein

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.

Author(s):  
B. E. Rhoades

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.


2011 ◽  
Vol 48 (3) ◽  
pp. 331-341 ◽  
Author(s):  
Mehmet Sarigöl

In the present paper, we characterize the classes of all triangular matrices, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $(|\bar N_p |,|\bar N_q^\theta |_k )$ \end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $(|\bar N_p^\theta |_k ,|\bar N_q |)$ \end{document} for the case k ≧ 1, where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $|\bar N_p^\theta |_k = \left\{ {a = (a_n ):\sum\limits_{n = 1}^\infty {\theta _n^{k - 1} } \left| {\frac{{p_n }}{{p_n p_{n - 1} }}\sum\limits_{v = 1}^n {P_{v - 1} a_v } } \right|^k < \infty } \right\},$ \end{document} i.e., the set of series summable by absolute weighted mean summability method, and so extend the some well known results.


2020 ◽  
Vol 70 (3) ◽  
pp. 681-688
Author(s):  
Bhikha Lila Ghodadra ◽  
Vanda Fülöp

AbstractIn this note, we obtain a Tauberian theorem for a class of regular lower triangular matrices operating on cosine series with coefficients tending to zero. As corollaries we obtain Tauberian theorems for weighted mean, Nörlund, and Hausdorff matrices.


Author(s):  
F. Móricz ◽  
B. E. Rhoades

We study the rate of approximation to functions inLpand, in particular, inLip(α,p)by weighted means of their Walsh-Fourier series, whereα>0and1≤p≤∞. For the casep=∞,Lpis interpreted to beCW, the collection of uniformlyWcontinuous functions over the unit interval[0,1). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.


Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2443-2449
Author(s):  
Şebnem Yıldız

By using a convex sequence Bor [H. Bor, Local properties of factored Fourier series, Appl. Math. Comp. 212 (2009) 82-85] has obtained a result dealing with local property of factored Fourier series for weighted mean summability. The purpose of this paper is to extend this result to more general cases by taking normal matrices in place of weighted mean matrices.


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