## Linear Operators: Spectral theory |

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Page 1223

How are we to choose its

the collection or of all functions with one continuous derivative. If f and g are any

two such functions, we have (iDs, g) = | if'(t):God = | f(t)igod Hi(f(1)g(I)-f(0.0) = (f, ...

How are we to choose its

**domain**? A natural first guess is to choose as**domain**the collection or of all functions with one continuous derivative. If f and g are any

two such functions, we have (iDs, g) = | if'(t):God = | f(t)igod Hi(f(1)g(I)-f(0.0) = (f, ...

Page 1249

Thus PP* is a projection whose range is 92 = Post, the final

complete the proof it will suffice to show that P*P is a projection if P is a partial

isometry. Let a, ve)', the initial

shows that ...

Thus PP* is a projection whose range is 92 = Post, the final

**domain**of P. Tocomplete the proof it will suffice to show that P*P is a projection if P is a partial

isometry. Let a, ve)', the initial

**domain**of P. Then the identity r +v? = |Pr-i-Pul”shows that ...

Page 1669

Let I, be a

I1 into I, such that (a) M-'C is a compact subset of I1 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 ...

Let I, be a

**domain**in E”, and let I, be a**domain**in E”. Let M : II – I, be a mapping ofI1 into I, such that (a) M-'C is a compact subset of I1 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 ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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 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