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Let $X$ and $Y$ are Banach spaces and $B(X, Y)$ be the Banach space of bounded linear operators from $X$ to $Y$.

I want to know the conditions under which imply that $B(X, Y)$ is separable? Please help.

J. W. Tanner
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    In the case of Hilbert spaces $B(X,Y)$ is separable iff $X$ is finite dimensional and $Y$ is separable or $Y$ is finite dimensional and $X$ is separable. – Kavi Rama Murthy Aug 26 '19 at 10:29
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    As Robert Israel pointed out here there exist infinite-dimensional separable Banach spaces $X,Y$ such that $\mathcal B(X,Y)$ is norm-separable. Generally speaking---at least this is the feeling I have---the situation for arbitrary Banach spaces seems to be very messy. – Frederik vom Ende Jan 02 '20 at 18:21

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