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 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
/ I ...
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
/ I ...
Page 872
complex variable that { Pn ( 2 ) } also converges uniformly on G . For each 1 in G
and each x in X define x ( a ) = lim Pn ( a ) where { Pn } is a ... For a fixed do e G
the map x + x ( 20 ) is a homomorphism of X into the field of complex numbers .
complex variable that { Pn ( 2 ) } also converges uniformly on G . For each 1 in G
and each x in X define x ( a ) = lim Pn ( a ) where { Pn } is a ... For a fixed do e G
the map x + x ( 20 ) is a homomorphism of X into the field of complex numbers .
Page 887
15 ) will yield , for normal operators in Hilbert space , a reduction theory which is
more complete than that developed in Chapter VII for general operators in a
complex B - space . Although the present chapter is independent of Chapter VII ,
it ...
15 ) will yield , for normal operators in Hilbert space , a reduction theory which is
more complete than that developed in Chapter VII for general operators in a
complex B - space . Although the present chapter is independent of Chapter VII ,
it ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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