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

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The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom most of the results

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom most of the results

**given**in Section 1 are due . B- and B * -algebras . The results of Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 ...Page 909

The proof follows immediately , for since LSM , we have ( Lx , x ) < ( Mx , x ) for every x in H. Hence the characterization of an , un

The proof follows immediately , for since LSM , we have ( Lx , x ) < ( Mx , x ) for every x in H. Hence the characterization of an , un

**given**in Theorem 3 shows that hn Mn for all n 2 , .... 1 , 5. Spectral Representation Let и M be a ...Page 1273

The simplification ,

The simplification ,

**given**by Freudenthal [ 3 ] , of Friedrichs ' proof is the one presented in the text . For another proof of the theorem , see Calkin 3 ] and Eberlein [ 2 ; p . 699 ) , and for applications to partial differential ...### 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 |

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