works of [@S] to the setting of infinite dimensional normed linear spaces. We extend Theorem $ 2.2 $ of [@S] completely, in case of compact linear operators defined on a reflexive Banach space. However, the scenario is far more complicated in case of general bounded linear operators defined on a normed linear space. At this point of our discussion, the following definitions are in order.

[@G] Let $ \mathbb{X} $ be a normed linear space and let $ x \in S_{\mathbb{X}}. $ We say that $ x $ is a rotund point of $ B_{\mathbb{X}} $ if $ \| y \| = \| \frac{x+y}{2} \| = 1 $ implies that $ x = y. $

A normed linear space $ \mathbb{X} $ is said to be strictly convex if for each $x,y \in S_{\mathbb{X}},$ $\|x+y\| < \|x\| + \|y\|$ whenever $x,y$ are linearly independent.

A normed linear space $ \mathbb{X} $ is said to be uniformly convex if to each $\epsilon, 0 < \epsilon \leq 2, $ there corresponds a $\delta(\epsilon) > 0$ such that the conditions $\|x\| = \|y\| = 1$ and $\|x - y \| > \epsilon $ imply $ \frac{\|x+y\|}{2} \leq  1-\delta(\epsilon).$

[@PSJ] Let $ \mathbb{X} $ 