## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 25

Page 611

The questions of

Schrödinger , but it is Rellich who ... In a series of five papers , Rellich [ 2 ]

considered the nature of the spectrum of the

the ...

The questions of

**perturbation**theory go back to the work of Lord Rayleigh and E.Schrödinger , but it is Rellich who ... In a series of five papers , Rellich [ 2 ]

considered the nature of the spectrum of the

**perturbed**operator , principally inthe ...

Page 612

both cases the

Nagy [ 2 , 4 ] gave different proofs for some of these results and extended some to

B - spaces ; further results in this general setting were obtained by Kato [ 1 , 2 ] ...

both cases the

**perturbation**depends analytically on a single parameter . Sz . -Nagy [ 2 , 4 ] gave different proofs for some of these results and extended some to

B - spaces ; further results in this general setting were obtained by Kato [ 1 , 2 ] ...

Page 772

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 .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero