QuestionDetails: Let H be a Hilbert spaceand X, Y be subspaces of H. Prove thefo

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QuestionDetails: Let H be a Hilbert spaceand X, Y be subspaces of H. Prove thefollowing: X, Y are closed subspaces andusing defintion: X = {y: < y, x > =0} (X   )  = X show that:                      QuestionDetails: Let H be a Hilbert spaceand X, Y be subspaces of H. Prove thefollowing: X, Y are closed subspaces andusing defintion: X = {y: < y, x > =0} X + Y = { x+y : x X, y Y }        (X   )  = X show that:                                                     1)  If X Y then Y  X                             2)(X + Y ) = X Y                                                  
3) (X   Y )   =X   + Y

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QuestionDetails: Let H be a Hilbert spaceand X, Y be subspaces of H. Prove thefo

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