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If $H$ is a Hilbert space and $T$ and $S$ are positive operators on $H$ (i.e. $ \ge 0$ and $ \ge 0$, for every $y \in H$ ) such that $T \le S$ (or $0 \le S-T$). Does it...
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It is known that a semisimple Banach algebra A whose multiplication is continuous (in both variables) with respect to the weak topology, is finite dimensional (see M. Akkar, E. Albrecht, L. Oubbi;...
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