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1. CMB 2010 (vol 53 pp. 398)
Projections in the Convex Hull of Surjective Isometries We characterize those linear projections represented as a convex combination of two surjective isometries on standard Banach spaces of continuous functions with values in a strictly convex Banach space.
Keywords:isometry, convex combination of isometries, generalized bi-circular projections Categories:47A65, 47B15, 47B37 |
2. CMB 2001 (vol 44 pp. 469)
Sums and Products of Weighted Shifts In this article it is shown that every bounded linear operator
on a complex, infinite dimensional, separable Hilbert space is
a sum of at most eighteen unilateral (alternatively, bilateral)
weighted shifts. As well, we classify products of weighted shifts,
as well as sums and limits of the resulting operators.
Categories:47B37, 47A99 |
3. CMB 2000 (vol 43 pp. 406)
Weighted Mean Operators on $l_p$ 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 Categories:47B37, 47A30, 40G05 |
4. CMB 1998 (vol 41 pp. 10)
Simple conditions for matrices to be bounded operators on $l_p$ The two theorems proved yield simple yet reasonably
general conditions for triangular matrices to be bounded
operators on $l_p$. The theorems are applied to N\"orlund and
weighted mean matrices.
Keywords:Triangular matrices, NÃ¶rlund matrices, weighted means, operators, on $l_p$. Categories:47B37, 47A30, 40G05 |
5. CMB 1998 (vol 41 pp. 49)
Stability of weighted darma filters We study the stability of linear filters associated with certain types of
linear difference equations with variable coefficients. We show that
stability is determined by the locations of the poles of a rational transfer
function relative to the spectrum of an associated weighted shift operator.
The known theory for filters associated with constant-coefficient difference
equations is a special case.
Keywords:Difference equations, adaptive $\DARMA$ filters, weighted shifts,, stability and boundedness, automatic continuity Categories:47A62, 47B37, 93D25, 42A85, 47N70 |