## Linear Operators: Spectral theory |

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Page 861

If T

Tole , then az = Tilz for every ze X. Also xa = T a = e = T : ' ( Te ) = T ; ' ( ex ) = ( T7'

e ) x Thus x - l

If T

**exists**in B ( X ) , then Te [ ( T ; ' y ) z ] = yz , ( T ? ' y ) 2 = 7 ' ( yz ) , and if a =Tole , then az = Tilz for every ze X. Also xa = T a = e = T : ' ( Te ) = T ; ' ( ex ) = ( T7'

e ) x Thus x - l

**exists**and T ; lz = x - 1z . 2 DEFINITION . An element « in a ...Page 1057

By Lemma 2 , the integral 0 ( tu )

( Vu )

( Vy ) \ yl - n eilu , u ) dy

By Lemma 2 , the integral 0 ( tu )

**exists**if 0 ( u )**exists**and t > 0 ; and the integral 0( Vu )

**exists**and equals 2 ( x ) ei ( x , Vu ) dx S. 2 ( Vy ) ei ( 1u ) dy En ly " if PSen 2( Vy ) \ yl - n eilu , u ) dy

**exists**and V is a rotation of E " . Thus , to show that the ...Page 1261

23 If an operator T has a closed linear extension there

linear extension T such that if T , is any closed linear extension of T then T CT , T

is called the closure of T. ( a ) There

23 If an operator T has a closed linear extension there

**exists**a unique closedlinear extension T such that if T , is any closed linear extension of T then T CT , T

is called the closure of T. ( a ) There

**exists**a densely defined operator with no ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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