Definition For Bounded Operators
Suppose H is a Hilbert space, with inner product . Consider a continuous linear operator A : H → H (this is the same as a bounded operator).
Using the Riesz representation theorem, one can show that there exists a unique continuous linear operator A* : H → H with the following property:
This operator A* is the adjoint of A. This can be seen as a generalization of the adjoint matrix of a square matrix which has a similar property involving the standard complex inner product.
Read more about this topic: Hermitian Adjoint
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