Predual

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 L1(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≅(A*)*) The predual A* induces a weak topology on A, under which algebra operations are separately weak continuous.[1]

## References

1. ↑ Ruan, Zhong-Jin (1992). "On the predual of dual algebras". Journal of Operator Theory 27 (1): 179–192. doi:10.2307/24715083.

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