In this paper, we study the factorability of linear time-varying (LTV) lossless filters and filter banks. We give a complete characterization of all degree-one lossless LTV systems and show that all degree-one lossless systems can be decomposed into a time-dependent unitary matrix followed by a lossless dyadicbased LTV system. The lossless dyadic-based system has several properties that make it...

We prove the norm identity ‖Id + T ‖ = 1 + ‖T ‖, which is known as the Daugavet equation, for weakly compact operators T on natural function spaces such as function algebras and L-predual spaces, provided a non-discreteness assumption is met. We also consider c0-factorable operators and operators on CΛ-spaces.

A fundamental result, due to Sabidussi and Vizing, states that every connected graph has a unique prime factorization relative to the Cartesian product; but disconnected graphs are not uniquely prime factorable. This paper describes a system of modular arithmetic on graphs under which both connected and disconnected graphs have unique prime Cartesian factorizations.

The following conjecture was posed by Axler and Shields. Let {xn} be a monotone decreasing sequence of nonnegative numbers, C the Cesáro matrix of order one. What is the best constant K for which ‖Cx‖2 ≥ K‖x‖2 for all such sequences {xn}? Lyons [3] determined that the best constant is π/ √ 6. This result was extended to p spaces for p > 1 by Bennett [1]. In [1], Bennett established the followin...

Recently, for single series, the necessary and sufficient conditions $\left\vert C,0\right\vert\Rightarrow \left\vert A_{f}\right\vert_{k}$ vise versa, A_{f}\right\vert \Rightarrow C,0\right\vert_{k}$ versa have been established, where $1 < k \infty $ $A$ is a factorable matrix. The present study extends these results to double summability, also provides some new results.