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To the best of my knowledge, among classical Banach spaces, $c^0,$ c_0,$ C[a,b], $L1[a,b],$ L_1[a,b],$ $l{\infinite}/c0$ l_{\infty}/c_0$ are not dual.

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To the best of my knowledge, among classical Banach spaces, $c^0,$ C[a,b], $L1[a,b],$ $l{\infinite}/c0$ are not dual.