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May 1, 2021 at 10:28 comment added Jack L. Perhaps it is straightforward to simply use that facts that (1) every compact set in an infinite dimensional Banach space has empty interior, (2) the closed convex hull of a compact set is compact, and (3) every infinite-dimensional separable Banach space is the closed linear span of a compact set (rather than going through the compact operators).
May 1, 2021 at 10:06 history undeleted Jack L.
May 1, 2021 at 10:01 history deleted Jack L. via Vote
May 1, 2021 at 10:01 history answered Jack L. CC BY-SA 4.0