Differential operators with the positive maximum property

On the Hyponormal Property of Operators

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...

A Maximum Principle for Positive Elliptic Pseudo-differential Operators on Closed Riemannian Manifolds

In this note we establish the positivity of Green’s functions for a class of elliptic differential operators on closed, Riemannian manifolds

Duality Property for Positive Weak Dunford-Pettis Operators

Weak Banach-Saks property in the space of compact operators

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

Maximum Codes with the Identifiable Parent Property

To my parents, my brothers and my husband. iii ACKNOWLEDGEMENTS There are many I would like to thank for helping me get this far. First and foremost are my family who carried the burden of supporting my study all these years. I thank them for their constant encouragement, loyal support, endless love, and for teaching me to take pride in myself. I will always be grateful for everything they have...