## Linear Operators: Spectral theory |

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Page 868

If I is a closed ideal in the commutative B - algebra X then the quotient algebra X /

I is isometrically isomorphic to the field of

maximal . PROOF . If 3 is not maximal it is properly contained in an ideal and so X

...

If I is a closed ideal in the commutative B - algebra X then the quotient algebra X /

I is isometrically isomorphic to the field of

**complex**numbers if and only if I ismaximal . PROOF . If 3 is not maximal it is properly contained in an ideal and so X

...

Page 872

and each x in X define x ( a ) = lim P ( 2 ) where { P , } is a sequence of

polynomials with P , ( z ) - x + 0. The number x ( ) is clearly independent of the

particular ...

**complex**variable that { Pņ ( 2 ) } also converges uniformly on G. For each 1 in Gand each x in X define x ( a ) = lim P ( 2 ) where { P , } is a sequence of

polynomials with P , ( z ) - x + 0. The number x ( ) is clearly independent of the

particular ...

Page 1157

k = 1 Then a

erists a function g which is analytic in a neighborhood of t and is such that g ( z ) =

| ( 2 ) for all z in this neighborhood for which [ 2 ] # 1 . Making use of this theorem

...

k = 1 Then a

**complex**number t of modulus 1 is outside o ( d ) if and only if thereerists a function g which is analytic in a neighborhood of t and is such that g ( z ) =

| ( 2 ) for all z in this neighborhood for which [ 2 ] # 1 . Making use of this theorem

...

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

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