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Anupam
Anupam
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We know that if $X$ is a separable Banach space, then for every infinite dimensional Banach space $Y$, there exists an injective compact operator from $X$ to $Y$.

My query is for every Banach space $X$ (need not be separable ) do there exist a Banach space $Y$ and an injective compact operator $T:X\to Y$?

We know that if $X$ is a separable Banach space, then for every Banach space $Y$, there exists an injective compact operator from $X$ to $Y$.

My query is for every Banach space $X$ (need not be separable ) do there exist a Banach space $Y$ and an injective compact operator $T:X\to Y$?

We know that if $X$ is a separable Banach space, then for every infinite dimensional Banach space $Y$, there exists an injective compact operator from $X$ to $Y$.

My query is for every Banach space $X$ (need not be separable ) do there exist a Banach space $Y$ and an injective compact operator $T:X\to Y$?

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Anupam
Anupam
  • 585
  • 2
  • 10

Existence of injective compact operators

We know that if $X$ is a separable Banach space, then for every Banach space $Y$, there exists an injective compact operator from $X$ to $Y$.

My query is for every Banach space $X$ (need not be separable ) do there exist a Banach space $Y$ and an injective compact operator $T:X\to Y$?