## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 884

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

most of the results

of Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 was proved ...

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 resultsof Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 was proved ...

Page 909

The proof follows immediately , for since L SM , we have ( Lx , x ) = ( Mx , x ) for

every æ in H. Hence the characterization of ini Men

that an SMen for all n - 1 , 2 , .... 5. Spectral Representation Let M be a finite

positive ...

The proof follows immediately , for since L SM , we have ( Lx , x ) = ( Mx , x ) for

every æ in H. Hence the characterization of ini Men

**given**in Theorem 3 showsthat an SMen for all n - 1 , 2 , .... 5. Spectral Representation Let M be a finite

positive ...

Page 1591

The defining property used by them coincides with the property we have

Theorem 4. The development followed in this section and the next , which makes

extensive use of Definition 1 , has also been used by Šnol [ 1 ] and Naïmark [ 5 ] ...

The defining property used by them coincides with the property we have

**given**inTheorem 4. The development followed in this section and the next , which makes

extensive use of Definition 1 , has also been used by Šnol [ 1 ] and Naïmark [ 5 ] ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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additive Akad 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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero