On $T$-orthogonality in Banach spaces

Abstract

Let $\mathbb X$ be a Banach space, and let $\mathbb X^*$ be the dual space of $\mathbb X$ and $T$ a bounded linear operator from $\mathbb X$ to $\mathbb X^*.$ For $x,y \in \mathbb X,$ $ x$ is said to be $T$-orthogonal to $y$ if $Tx(y) =0$. We study the no