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

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Page 868

If I is a closed ideal in the commutative B - algebra X then the quotient algebra X / 3 is isometrically isomorphic to the field of

If I is a closed ideal in the commutative B - algebra X then the quotient algebra X / 3 is isometrically isomorphic to the field of

**complex**numbers if and only if I is marimal . Proof . If I is not maximal it is properly contained in an ...Page 872

n a

n a

**complex**variable that { Pn ( 2 ) } also converges uniformly on G. For each 2 in G and each x in X define x ( a ) = lim P ( 2 ) where { P } is a sequence of polynomials with P , ( z ) -2 +0 . The number x ( 2 ) is clearly independent ...Page 1157

k = 1 Then a

k = 1 Then a

**complex**number t of modulus 1 is outside o ( d ) if and only if there exists a function g which is analytic in a neighborhood of t and is such that g ( 2 ) = f ( z ) for all in this neighborhood for which 121 + 1 .### 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