Predual
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In mathematics, the predual of an object D is an object P whose dual space is D. For example, the predual of the space of bounded operators is the space of trace class operators, and the predual of the space L ∞ (R) of essentially bounded functions on R is the Banach space L 1 (R) of integrable functions. In operator algebra, if a dual Banach/operator space A is realized as the dual of some Banach space A_* , then A_* is called the predual of A (formally: A \cong (A_* )^* ). The predual A_* induces a weak topology on A , under which algebra operations are separately weak continuous.
In mathematics, the predual of an object D is an object P whose dual space is D. For example, the predual of the space of bounded operators is the space of trace class operators, and the predual of the space L ∞ (R) of essentially bounded functions on R is the Banach space L 1 (R) of integrable functions. In operator algebra, if a dual Banach/operator space A is realized as the dual of some Banach space A_* , then A_* is called the predual of A (formally: A \cong (A_* )^* ). The predual A_* induces a weak topology on A , under which algebra operations are separately weak continuous. ==References==
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