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I believe that part of Greg Kuperberg's answer to this other questionthis other question answers your question by showing that no such "explicit" functional exists. Namely, he cites an assertion in an article by N. Brunner that implies that continuity of all functionals on all Banach spaces is consistent with ZF (a more precise statement is found at the link).

I believe that part of Greg Kuperberg's answer to this other question answers your question by showing that no such "explicit" functional exists. Namely, he cites an assertion in an article by N. Brunner that implies that continuity of all functionals on all Banach spaces is consistent with ZF (a more precise statement is found at the link).

I believe that part of Greg Kuperberg's answer to this other question answers your question by showing that no such "explicit" functional exists. Namely, he cites an assertion in an article by N. Brunner that implies that continuity of all functionals on all Banach spaces is consistent with ZF (a more precise statement is found at the link).

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Jonas Meyer
Jonas Meyer
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I believe that part of Greg Kuperberg's answer to this other question answers your question by showing that no such "explicit" functional exists. Namely, he cites an assertion in an article by N. Brunner that implies that continuity of all functionals on all Banach spaces is consistent with ZF (a more precise statement is found at the link).