## Linear Operators: Spectral theory |

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Results 1-3 of 82

Page 1175

Then x^i is a bounded

real So, let /, be the

5 - 5, 0 otherwise. By Corollary 22, it follows that there is a finite constant C" such

...

Then x^i is a bounded

**mapping**of the space L,(L,(S)) into itself. Proof. For eachreal So, let /, be the

**mapping**in L,(L,(S)) defined by the formula (47) (*,f)(3) = f(5),5 - 5, 0 otherwise. By Corollary 22, it follows that there is a finite constant C" such

...

Page 1669

Let M : II – I, be a

whenever C is a compact subset of I2; (b) (M(.)), e C*(I), j = 1,..., n2. Then (i) for

each p in C*(I2), p o M will denote the function p in C*(II) defined, for a in II, by the

...

Let M : II – I, be a

**mapping**of I1 into I, such that (a) M-'C is a compact subset of I1whenever C is a compact subset of I2; (b) (M(.)), e C*(I), j = 1,..., n2. Then (i) for

each p in C*(I2), p o M will denote the function p in C*(II) defined, for a in II, by the

...

Page 1707

Hence, by Lemma 3.41, to-i-A is a continuous

of Hot”(C) onto Ho (C), for all k between – o and + o. Let ve and so be the norms

of the

Hence, by Lemma 3.41, to-i-A is a continuous

**mapping**with a continuous inverseof Hot”(C) onto Ho (C), for all k between – o and + o. Let ve and so be the norms

of the

**map**to-1-2 : Hot" (C) → Ho (C) and of its inverse, respectively. Let vi = to ...### 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 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero