Suppose T 2 L.V / is self-adjoint, 2 F, and >0. Suppose thereexists v 2 V such that kvk

Chapter 7, Problem 12

(choose chapter or problem)

Suppose T 2 L.V / is self-adjoint, 2 F, and >0. Suppose thereexists v 2 V such that kvk D 1 andkT v vk < :Prove that T has an eigenvalue 0 such that j 0j < .

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