## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 877

**COROLLARY**. A commutative B * -algebra of operators in Hilbert space is isometrically * -equivalent to the B * -algebra of all continuous functions on its spectrum .**COROLLARY**. Let y be a B * -subalgebra of the commutative B * -algebra ...Page 898

If we put E ( S ) = 0 when d no ( T ) is void , then

If we put E ( S ) = 0 when d no ( T ) is void , then

**Corollary**4 follows immediately from Theorem 1 and**Corollary**IX.3.15 . Q.E.D. 5 DEFINITION . The uniquely defined spectral measure associated , in**Corollary**4 , with the normal ...Page 1301

However , as vo satisfies an equation of order 2n , v , must be identically zero . This contradiction completes the proof . Q.E.D. ( ) τ 23

However , as vo satisfies an equation of order 2n , v , must be identically zero . This contradiction completes the proof . Q.E.D. ( ) τ 23

**COROLLARY**. Let T be a formal differential operator of order n on an interval I with end points ...### What people are saying - Write a review

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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero