Abstract view
Weighted Mean Operators on $l_p$


Published:20001201
Printed: Dec 2000
Abstract
The weighted mean matrix $M_a$ is the triangular matrix $\{a_k/A_n\}$,
where $a_n > 0$ and $A_n := a_1 + a_2 + \cdots + a_n$. It is proved
that, subject to $n^c a_n$ being eventually monotonic for each
constant $c$ and to the existence of $\alpha := \lim
\frac{A_n}{na_n}$, $M_a \in B(l_p)$ for $1 < p < \infty$ if and only
if $\alpha < p$.
MSC Classifications: 
47B37, 47A30, 40G05 show english descriptions
Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) Norms (inequalities, more than one norm, etc.) Cesaro, Euler, Norlund and Hausdorff methods
47B37  Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47A30  Norms (inequalities, more than one norm, etc.) 40G05  Cesaro, Euler, Norlund and Hausdorff methods
