## Linear Operators: Spectral theory |

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Page 952

8 and the regularity of 2 that the collection of functions which are

vanish outside of compact sets is dense in L , ( R ) . Hence for f in L , ( R ) let k be

such a

8 and the regularity of 2 that the collection of functions which are

**continuous**andvanish outside of compact sets is dense in L , ( R ) . Hence for f in L , ( R ) let k be

such a

**continuous**function with 1 - klo < € . Since k is uniformly**continuous**, we ...Page 968

The one - to - one mapping m → hm , whose existence was established in

Theorem 11 , is a homeomorphism of Mo onto Â . Proof . We first show that the

mapping m hm is

let N ...

The one - to - one mapping m → hm , whose existence was established in

Theorem 11 , is a homeomorphism of Mo onto Â . Proof . We first show that the

mapping m hm is

**continuous**. Let me be an arbitrary point in Mo , 0 < e < 1 , andlet N ...

Page 1903

6 ( 428 ) criteria for existence of

- existence in Lp , 0 < p < 1 , 1 . 7 . 37 ( 438 )

Absolutely

6 ( 428 ) criteria for existence of

**continuous**linear functionals , V . 7 . 3 ( 436 ) non- existence in Lp , 0 < p < 1 , 1 . 7 . 37 ( 438 )

**Continuous**functions . ( See alsoAbsolutely

**continuous**functions ) as a B - space , additional properties , IV .### What people are saying - Write a review

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### 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