Based on here, I know that every bounded and closed subset of a space is not compact. I really want to know that $B(H)$, the space of bounded linear operators, satisfies in Heine - Borel property. Please help me.
Thanks.
2026-03-29 20:50:51.1774817451
Does $B(H)$ satisfy in Heine-Borel property?
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Any infinite dimensional normed space lacks Heine-Borel property, because by corollary of Riesz theorem about almost perpendicular the unit ball of infinite dimensional normed space is not compact.