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

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Page 875

It will also be shown that this

It will also be shown that this

**isomorphism**is a * -**isomorphism**, i.e. , one preserving the operation of involution . This basic result , which is due to Gelfand and Naïmark , will find many applications in the next two chapters .Page 878

one * -

one * -

**isomorphism**of B * ( r ) onto C ( o ( x ) ) into another one . There is one isometric * -**isomorphism**of B * ( x ) onto C ( o ( x ) ) that we wish to single out . In the notation of the preceding proof the * -**isomorphism**y + y ( x ...Page 1373

of L2 ( 1 , { Pv ; } ) into L2 ( 1 , { ij } ) and an isometric

of L2 ( 1 , { Pv ; } ) into L2 ( 1 , { ij } ) and an isometric

**isomorphism**of L2 ( 1 , { ui ; } ) into L2 ( 1 , { llij ) . ... A and B are isometric**isomorphisms**onto all of L ( 1 , { fii } ) and L2 ( 1 , { Mis } ) , respectively .### 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