## Linear Operators: Spectral operators |

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Page 2025

Since Ex : ( 8 ) # 0 there is a vector 4 ( 8 ) in EP with [ 4 ( 8 ) = 1 and f ( s ) = Êk ; ( )

{ ( s ) . Thus , since Êky ( s ) and Êkg ( s ) are disjoint projections if q # j , it follows

from ( 35 ) that R ( ) ; Â ( s ) ) " } ( s ) = 4 ( s ) ( a - dxj ( s ) ) - n and ( 39 )

Since Ex : ( 8 ) # 0 there is a vector 4 ( 8 ) in EP with [ 4 ( 8 ) = 1 and f ( s ) = Êk ; ( )

{ ( s ) . Thus , since Êky ( s ) and Êkg ( s ) are disjoint projections if q # j , it follows

from ( 35 ) that R ( ) ; Â ( s ) ) " } ( s ) = 4 ( s ) ( a - dxj ( s ) ) - n and ( 39 )

**gives**cv ...Page 2031

To prove ( iv ) suppose first that y is in 0 in which case a permissible interchange

of integration

ds = Tru ( Q ) , QeQ . RN Now 0 is dense in H = L2 ( RN ) and thus there is for an

...

To prove ( iv ) suppose first that y is in 0 in which case a permissible interchange

of integration

**gives**" RN " ( FT . ) ( o ) = S ( FC ) ( 9 ) 4 ( 8 ) ds = 0 ( s ) ( F % ) ( s )ds = Tru ( Q ) , QeQ . RN Now 0 is dense in H = L2 ( RN ) and thus there is for an

...

Page 2065

Thus the Gelfand theory

not an element possesses an inverse and so ... In order to apply this procedure to

a given algebra , it is sufficient to

...

Thus the Gelfand theory

**gives**a general procedure for determining whether ornot an element possesses an inverse and so ... In order to apply this procedure to

a given algebra , it is sufficient to

**give**a satisfactory representation of its spectrum...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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