{{short description|Banach space of a dual}} {{One source|date=March 2026}} 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.<ref>{{cite journal | last = Ruan | first = Zhong-Jin | year = 1992 | title = On the predual of dual algebras | journal = Journal of Operator Theory | volume = 27 | issue = 1 | pages = 179–192 | doi = 10.2307/24715083 }}</ref>
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==References== {{reflist}}
Category:Abstract algebra Category:Functional analysis
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