In the case of a finite-dimensional linear space L, the dual, or conjugate, space L* consisting of all linear functionals on L plays an important role in the general theory. The primary result in the finite-dimensional case is that the natural injection of L into the dual L** of L is an isomorphism of L onto L**. This means that if x is an element of L and x** denotes the element of L** given by the equation x**(f) = f(x) for all f in L*, then the map x → x** is one-to-one from L onto L**.
KeywordsBanach Space Measure Space Linear Functional Weak Topology Continuous Linear
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