Consider the Hilbert space H = Let (X, , μ) be a o-finite measure space. L²(X, N, μ) =: L² (µ). If ¢ € L∞ (μµ), define M : L² (μ) → L² (μ) by Mof=of. (a) Show that Mo B(H) and ||Mo|| = ||||. Here is the u-essential supremum norm. Mō. (b) Show that Mr = (c) Show that Mo is normal. When Mo is self adjoint? unitary?

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