its an humble request to solve all questions.Functional analyais

Q2(ii) Let (X, ) be an inner product space. Let x(# 0), y(# 0) ( X such that xly. Show that {x, y} is a linearly independent set in X. Q3(i) Let (X, ) be a Hilbert space and TE BL(X, X) be a bijective map whose inverse is bounded. Prove that (a) (T') exists; (b) (T*)= (T-] )*. Q3(ii) Let (X, ) be a Hilbert space. Let {T.} C BL(X, X) be a sequence of normal operators and T - T. Prove that T is also a normal linear operator