In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, the predual of an object ''D'' is an object ''P'' whose
dual space
In mathematics, any vector space ''V'' has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on ''V'', together with the vector space structure of pointwise addition and scalar multiplication by const ...
is ''D''.
For example, the predual of the space of
bounded operator
In functional analysis and operator theory, a bounded linear operator is a linear transformation L : X \to Y between topological vector spaces (TVSs) X and Y that maps bounded subsets of X to bounded subsets of Y.
If X and Y are normed vector s ...
s is the space of
trace class In mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a Trace (linear algebra), trace may be defined, such that the trace is a finite number independent of the choice of basis used to compute the tra ...
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..
Abstract algebra
Functional analysis
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