Linear Operators, Part 2 |
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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 complex numbers if and only if I is
maximal . PROOF . If I is not maximal it is properly contained in an ideal and so X
/ 3 ...
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 is
maximal . PROOF . If I is not maximal it is properly contained in an ideal and so X
/ 3 ...
Page 872
complex variable that { Po ( 2 ) } also converges uniformly on G . For each 2 in G
and each x in X define x ( a ) = lim Pm ( a ) where { P , } is a sequence of
polynomials with \ P . , ( z ) — « \ + 0 . The number x ( 2 ) is clearly independent of
the ...
complex variable that { Po ( 2 ) } also converges uniformly on G . For each 2 in G
and each x in X define x ( a ) = lim Pm ( a ) where { P , } is a sequence of
polynomials with \ P . , ( z ) — « \ + 0 . The number x ( 2 ) is clearly independent of
the ...
Page 1157
Then a complex number t of modulus 1 is outside old ) if and only if there exists a
function g which is analytic in a neighborhood of t and is such that g ( x ) = f ( z )
for all z in this neighborhood for which 121 + 1 . Making use of this theorem and ...
Then a complex number t of modulus 1 is outside old ) if and only if there exists a
function g which is analytic in a neighborhood of t and is such that g ( x ) = f ( z )
for all z in this neighborhood for which 121 + 1 . Making use of this theorem and ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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