Symmetrizable compact operator

In functional analysis, particularly in the context of operator theory, a **symmetrizable compact operator** is a specific type of bounded linear operator defined on a Hilbert space (or more generally, a Banach space) that satisfies certain symmetry properties. A compact operator \( T \) on a Hilbert space \( H \) is an operator such that the image of any bounded set under \( T \) is relatively compact, meaning its closure is compact.