Assuming the continuum hypothesis, there are infinite-dimensional real and complex Banach spaces with no bounded linear surjection onto any infinite-dimensional separable Banach space.
Assuming the continuum hypothesis, there are infinite-dimensional real and complex Banach spaces with no bounded linear surjection onto any infinite-dimensional separable Banach space.
Assuming the continuum hypothesis, there are infinite-dimensional real and complex Banach spaces with no bounded linear surjection onto any infinite-dimensional separable Banach space.
If correct, establishes failure of the separable quotient assertion under the continuum hypothesis.
Can every infinite-dimensional Banach space have an infinite-dimensional separable quotient under CH?
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OpenAI reports CH counterexamples to the separable quotient property
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