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

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Page 875

It will be

It will be

**shown**that the homomorphism x + x ( • ) ( see Theorem 2.9 ) of a commutative B * -algebra X into the algebra C ( 1 ) of all continuous functions on the structure space 1 of X is an isometric isomorphism of X onto all of C ( 1 ) ...Page 981

If H ( T ( ) ) does not vanish identically for f in Ly ( R ) then , as was

If H ( T ( ) ) does not vanish identically for f in Ly ( R ) then , as was

**shown**in the first part of the proof of Theorem 3.11 , there is a continuous character h on R with H , ( T ( j ) ) = Sxh ( x ) f ( x ) dx , feLi ( R ) .Page 1161

That spectral synthesis is not possible for all functions in Lo was

That spectral synthesis is not possible for all functions in Lo was

**shown**by L. Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been**shown**by M. Paul Malliavin that spectral synthesis is not possible for all ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### 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