Okay, I've been trying to understand the spectral mapping theorem. So x is an operator, σ(x) is its spectrum, and f(x) is some function. Suppose σ(x) = [0, 1], and f(x) = x^{2}  3I. Then the spectral mapping theorem says that the spectrum of the operator A = x^{2}  3I is given by the image of f(y) = y^{2}  3 on y[itex]\in[/itex][0, 1], which in this case would be [3, 2]. Is this right?
