## Linear Operators: Spectral theory |

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Page 1826

Unconditional convergence in

- 152 ( 1948 ) . 2 . Bases in

) . Kato , T . 1 . On the convergence of the perturbation method , I , II .

Unconditional convergence in

**Banach spaces**. Bull . Amer . Math . Soc . 54 , 148- 152 ( 1948 ) . 2 . Bases in

**Banach spaces**. Duke Math . J . 15 , 971 - 985 ( 1948) . Kato , T . 1 . On the convergence of the perturbation method , I , II .

Page 1844

Absolute and unconditional convergence in

351 - 365 ( 1946 ) . Introduction to measure and integration . Addison Wesley ,

Cambridge , Mass . , 1953 . A note on weak differentiability of Pettis integrals .

Absolute and unconditional convergence in

**Banach spaces**. Duke Math . J . 13 ,351 - 365 ( 1946 ) . Introduction to measure and integration . Addison Wesley ,

Cambridge , Mass . , 1953 . A note on weak differentiability of Pettis integrals .

Page 1871

16 . Eigenfunction expansions associated with second - order differential

equations . Oxford Univ . Press , London , 1946 . Titov , N . S . 1 . On different

kinds of convergence of elements and linear operators in

Doklady Akad .

16 . Eigenfunction expansions associated with second - order differential

equations . Oxford Univ . Press , London , 1946 . Titov , N . S . 1 . On different

kinds of convergence of elements and linear operators in

**Banach spaces**.Doklady Akad .

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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### Common terms and phrases

additive adjoint operator Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f 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 Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero