## Linear Operators: Spectral theory |

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Page 921

may be extended in case the operators considered are normal operators on

Hilbert space . In this section we shall be concerned with

strong ...

**Perturbation**Theory The general**perturbation**theory discussed in Section VII.6may be extended in case the operators considered are normal operators on

Hilbert space . In this section we shall be concerned with

**perturbation**in thestrong ...

Page 1826

Karlin , s . 1 . 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

Karlin , s . 1 . 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 1916

... fundamental theorem on , I.2.5 ( 5 ) study of , 1.2 totally ordered , 1.2.2 ( 4 ) well

ordered , I.2.8 ( 7 ) Periodic function ( almost periodic function ) , definition , IV.

2.25 ( 242 ) multiply , IV.14.68 ( 367 ) study of , IV.7

linear ...

... fundamental theorem on , I.2.5 ( 5 ) study of , 1.2 totally ordered , 1.2.2 ( 4 ) well

ordered , I.2.8 ( 7 ) Periodic function ( almost periodic function ) , definition , IV.

2.25 ( 242 ) multiply , IV.14.68 ( 367 ) study of , IV.7

**Perturbation**of boundedlinear ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently 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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero