Summary: 6 Classical dualities and reflexivity
1. Classical dualities. Let (, A, µ) be a measure space. We will describe
the duals for the Banach spaces Lp
() .
First, notice that any f Lp
, 1 p , generates the linear functional
Ff on Lp
by the rule
Ff (u) =

uf dµ, u Lp
.
Indeed, by the Hölder inequality
|Ff (u)| =

fu dµ
f p u p.
Thus Ff f p . Consequently the mapping
Ip : Lp
- Lp

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics