## Linear Operators: Spectral theory |

### From inside the book

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Page 1176

Let p, q, k, be as in the preceding lemma, and, for each N, let X^N be the

transformation in L,(l,) which maps the

Fourier transform f,($) into the

transform k,($)f ...

Let p, q, k, be as in the preceding lemma, and, for each N, let X^N be the

transformation in L,(l,) which maps the

**vector**whose nth component has theFourier transform f,($) into the

**vector**whose nth component has the Fouriertransform k,($)f ...

Page 1837

Bicontinuous linear transformations in certain

Soc. 45, 564-569 (1939). 2. On a calculus of operators in reflerive

Trans. Amer. Math. Soc. 45, 217–234 (1939). 3. The Cauchy-Schwarz inequality

...

Bicontinuous linear transformations in certain

**vector**spaces. Bull. Amer. Math.Soc. 45, 564-569 (1939). 2. On a calculus of operators in reflerive

**vector**spaces.Trans. Amer. Math. Soc. 45, 217–234 (1939). 3. The Cauchy-Schwarz inequality

...

Page 1849

Compact metric Boolean algebras and

A. 11, 125–128 (1942). 2. On Fréchet lattices, I. J. Sci. Hirosima Univ. Ser. A. 12,

235–248 (1943). (Japanese) Math. Rev. 10, 544 (1949). 3. Remarks on a

Compact metric Boolean algebras and

**vector**lattices. J. Sci. Hirosima Univ. Ser.A. 11, 125–128 (1942). 2. On Fréchet lattices, I. J. Sci. Hirosima Univ. Ser. A. 12,

235–248 (1943). (Japanese) Math. Rev. 10, 544 (1949). 3. Remarks on a

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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