Question: Let : be a bounded linear operator on a complex inner product space . If < , > = for all , show that =

Let : be a bounded linear operator on a complex inner product space . If < , > = for all , show that = . Show that this does not hold in the case of a real inner product space.

Let the operator : be defined by = + , , where = , . Find . Show that we have = = . Find = ( + ) and = ( ).

Show that a projection in a Hilbert space is an orthogonal projection if and only if () ().

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