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 P: 318 The answer: There is no compact (continuous) injective operator on a non separable hilbert space. Quick demo: H the hilbert space. T the compact injective operator => Closure[T(H)] is a separable space (compacity property) => there is no injection between a non separable hilbert space and the separable one. Moreover, we have a weaker formulation of this impossibility: there is no injective compact operator between a non separable Hilbert space and any banach space. (i.e. we can have an injective compact operator between 2 banach spaces, even if the banach spaces are non separable). Seratend.