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Feb27-12, 07:47 PM
P: 29
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) = x2 - 3I. Then the spectral mapping theorem says that the spectrum of the operator A = x2 - 3I is given by the image of f(y) = y2 - 3 on y[itex]\in[/itex][0, 1], which in this case would be [-3, -2]. Is this right?