Recent content by sfire

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Let A be a bounded operator in complex Hilbert space. Prove that \sigma(Exp(A))=Exp(\sigma(A)). It is known, that \sigma(P(A))=P(\sigma(A)), where P is a polynomial. In addition, if an operator A has a bounded inverse, then for any operator B such that ||B||<1/||A^{-1}|| their sum A+B...