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In this MSE and question and this MO question, stronger variants of the classical Cauchy-Schwarz inequality have been suggested in finite dimensional spaces. Can we find similar results for infinite ...

Let $X,Y$ be finite-dimensional real normed spaces. Consider the set of linear operators $L(X,Y)$ between the two spaces. Then we define the set of equivalence classes $$G(X,Y):=\left\{[T]; T,S \in ...

Given $d<k$. Let ${\cal M}_{d\times k}(\mathbb{R})$ denotes the set of all $d\times k$ real matrices and suppose that $H:\mathbb{R}^k\rightarrow {\cal M}_{d\times k}(\mathbb{R})$ is a continuous ...