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A note on compact operators which attain their norm

A note on compact operators which attain their norm

For Banach spaces X having the unit cell of X**w*sequentially compact, the compact operators from X into a Banach space Y attain their norm in X**.The same holds for weakly compact operators if, in addition, X has the strict Dunford-Pettis property.For Banach spaces X such that the quotient space X**/X …