Let M be an anti-self-adjoint operator and L(s) be a family of operators satisfying the equation 0,L(s) = [M, L] %3D where [M, L] = ML - LM. Show that: 1. If the operator Lo is self-adjoint then L(s)...

Let M be an anti-self-adjoint operator and L(s) be a family of operators satisfying<br>the equation<br>0,L(s) = [M, L]<br>%3D<br>where [M, L] = ML - LM. Show that:<br>1. If the operator Lo is self-adjoint then L(s) is self-adjoint for any s.<br>2. The operators L(s) and Lo have the same spectrum.<br>

Extracted text: Let M be an anti-self-adjoint operator and L(s) be a family of operators satisfying the equation 0,L(s) = [M, L] %3D where [M, L] = ML - LM. Show that: 1. If the operator Lo is self-adjoint then L(s) is self-adjoint for any s. 2. The operators L(s) and Lo have the same spectrum.

Jun 05, 2022

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Let M be an anti-self-adjoint operator and L(s) be a family of operators satisfying the equation 0,L(s) = [M, L] %3D where [M, L] = ML - LM. Show that: 1. If the operator Lo is self-adjoint then L(s)...

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