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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 $g(t)$ be a convex positive function. I'm trying to show that the set $\{ |t|^ne^{\frac{g(t)}{t^n}}\}_{n\in \mathbb{N}}$ is linearly independent in the space of measurable functions on $\mathbb{R}...

Let $X$ be a continuous linear self-adjoint operator on some Hilbert space $H$ and for arbitrary compact operators $A$ we have: $XA+AX=0.$ Does this imply that $X=0$ or can there be non-trivial ...