## Linear Operators: Spectral theory |

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Page 1425

It follows from the

in [ a , o ) , k max \ | ( s ) [ 2 max f ' ( s ) . asostm asosim Indeed , if this were not the

case , then to every integer m we could associate a point tm in [ a , 0 ) such ...

It follows from the

**preceding**lemma that there exists a constant k such that for all tin [ a , o ) , k max \ | ( s ) [ 2 max f ' ( s ) . asostm asosim Indeed , if this were not the

case , then to every integer m we could associate a point tm in [ a , 0 ) such ...

Page 1437

Suppose that a bounded sequence { In } of elements of D ( T . ( T ) ) exists such

that { ( 7 - hotn } converges but the sequence { n } has no convergent

subsequence . Then , since T . ( T ) C Ti ( t ) , it follows immediately from the

Suppose that a bounded sequence { In } of elements of D ( T . ( T ) ) exists such

that { ( 7 - hotn } converges but the sequence { n } has no convergent

subsequence . Then , since T . ( T ) C Ti ( t ) , it follows immediately from the

**preceding**lemma ...Page 1469

Thus statement ( a ) follows immediately from the

statement ( b ) , note that r is finite below ho , but not below any a > 20 . Statement

( b ) then follows immediately from the

...

Thus statement ( a ) follows immediately from the

**preceding**lemma . To provestatement ( b ) , note that r is finite below ho , but not below any a > 20 . Statement

( b ) then follows immediately from the

**preceding**lemma . Q . E . D . Next we turn...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero