Let M be an anti-self-adjoint operator and L(s) be a family of operators satisfyingthe equation0,L(s) = [M, L]%3Dwhere [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.

Use the given two equations to prove the following. If one operator is self-adjoint, then use the…

Answered: Let M be an anti-self-adjoint operator…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let M be an anti-self-adjoint operator and L(s) be a family of operators satisfying the equation 8,L(s) = [M, L] 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.