Unit ball of the adjoint space of a separable Banach space is second-countable in the weak* topology.

Asked Feb 04 '18 at 05:42

Active Feb 04 '18 at 06:55

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In the proof : If $A$ is separable, then $\Delta(A)$ satisfies the second axiom of countability. ($\Delta(A)$ the set of all complex homomorphisms of $A$.)

I have found they says "It is easy to see that the unit ball of the adjoint space of a separable Banach space is second-countable in the weak* topology."

But I do not find verifying it trivial, Need some hints to do it.

edited Feb 04 '18 at 06:55

Martin Sleziak

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asked Feb 04 '18 at 05:42

User8976

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Some related questions: If X is separable, then ball $X^*$ is weak-star metrizable. and Unit ball in dual space is weak*separable – Martin Sleziak Feb 04 '18 at 06:55

Unit ball of the adjoint space of a separable Banach space is second-countable in the weak* topology.

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