Linear expand-contract plasticity of ellipsoids revisited

This work is aimed to describe linearly expand-contract plastic ellipsoids given via quadratic form of a bounded positively defined self-adjoint operator in terms its spectrum.Let $Y$ be metric space and $F\colon Y\to Y$ map. $F$ called non-expansive if it does not increase distance between points the $Y$. We say that subset $M$ normed $X$ (briefly an LEC-plastic) every linear $T\colon X \to X$ whose restriction on bijection from onto isometry $M$.In paper, we consider fixed separable infinite-dimensional Hilbert $H$. define ellipsoid $H$ as set following $E =\left\{x \in H\colon \left\langle x, Ax \right\rangle \le 1 \right\}$ where $A$ for which holds: $\inf_{\|x\|=1} Ax,x\right\rangle >0$ $\sup_{\|x\|=1} < \infty$.We provide example demonstrates spectrum generating has non empty continuous part, then such plastic.In this work, also proof only part eigenvalues consists more than one element either maximum finite multiplicity or minimum multiplicity.