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<sup>∞</sup>(R) of essentially bounded functions on R is the Banach space L<sup>1</sup>(R) of integrable functions.
In operator algebra, if a dual Banach/operator space <math>A</math> is realized as the dual of some Banach space <math>A_*</math>, then
<math>A_*</math> is called the predual of <math>A</math> (Formally: <math>A \cong (A_* )^*</math>)
The predual <math>A_*</math> induces a weak topology on <math>A</math>, under which algebra operations are separately weak continuous.
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