## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 861

If Til

Tote , then az = To'z for every z e X. Also Tea = e = T ... An element « in a B -

algebra X is said to be regular in case x - 1

regular .

If Til

**exists**in B ( X ) , then Tx [ ( T2 + y ) 2 ] = yz , ( To'y ) 2 = 7 ; ' ( yz ) , and if a =Tote , then az = To'z for every z e X. Also Tea = e = T ... An element « in a B -

algebra X is said to be regular in case x - 1

**exists**in X. It is singular if it is notregular .

Page 1057

Thus ( 2 ) gives 2 ( y ) F ( K * / ) ( u ) ( 21 ) -1/2 lim P S. X ; ( y ) { S efur f ( x − y ) dx

) day ER 2 ( y ) lim P Jgn lyn ZA ( Y ) e'wv dy } F ( ) ( u ) , provided only that the

limit in the braces in this last equation

Thus ( 2 ) gives 2 ( y ) F ( K * / ) ( u ) ( 21 ) -1/2 lim P S. X ; ( y ) { S efur f ( x − y ) dx

) day ER 2 ( y ) lim P Jgn lyn ZA ( Y ) e'wv dy } F ( ) ( u ) , provided only that the

limit in the braces in this last equation

**exists**. Thus , to complete the proof of 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 ICT . T is

called the closure of T. ( a ) There

closed ...

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 ICT . T is

called the closure of T. ( a ) There

**exists**a densely defined operator with noclosed ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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