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

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Page 861

Clearly if x - 1

Clearly if x - 1

**exists**then Tr - Tc = T / T2-1 = 1 . 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 ; ' ( Tee ) = T ...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**.Page 1261

23 If an operator T has a closed linear extension there

23 If an operator T has a closed linear extension there

**exists**a unique closed 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**exists**a densely defined ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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