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Weighted Mean Operators on $l_p$ |
Published:2000-12-01
Printed: Dec 2000
Printed: Dec 2000
- David Borwein
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 $\alpha < p$.
| Keywords: | weighted means, operators on $l_p$, norm estimates |
| MSC Classifications: |
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 |