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Simplifying Proofs in Spectral Theory

The problem revolves around finding a more direct proof for the fact that the spectrum of a polynomial P(z,z*) applied to a normal operator T on a Hilbert space is the same as the image of P on the spectrum of T, without relying heavily on the spectral theorem and Riesz-Markov-Kakutani theorem.

Mathematics & logic, Mathematics, Mathematical Logic