## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 86

Page 875

It will be

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 ( 4 ) .

It will be

**shown**that the homomorphism x + x ( • ) ( see Theorem 2 . 9 ) of acommutative 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 ( 4 ) .

Page 981

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

first part of the proof of Theorem 3 . 11 , there is a continuous character h on R

with H , ( T ( 1 ) ) = Sah ( x ) f ( x ) dx , feLi ( R ) . The converse part of Theorem 3 .

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

**shown**in thefirst part of the proof of Theorem 3 . 11 , there is a continuous character h on R

with H , ( T ( 1 ) ) = Sah ( x ) f ( x ) dx , feLi ( R ) . The converse part of Theorem 3 .

Page 1161

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

Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been

on the ...

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 functionson the ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### 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 consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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