Question: 4. Let Vi and Va be two Hilbert spaces with the inner products (, .), and (, )v2, respectively. Let T : Vi - V2

4. Let Vi and Va be two Hilbert spaces with the inner products (, .), and (, )v2, respectively. Let T : Vi - V2 be a bounded linear operator, and let 7"* be the adjoint operator of T, i.e., (To, y) v. = (x, T*y)v, for any x e V1 and y e V2. (a) Prove that 7* is a linear operator. (b) Prove that (7* )* = T. (c) Prove that |7"* ||

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