## Linear Operators: General theory |

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Page 45

Expressed differently , the cofactor of aij is

by 1 and all the other elements of the ith row and jth column by 0 and calculating

the resulting determinant . Denoting the cofactor of aig by Ais , it may be seen ...

Expressed differently , the cofactor of aij is

**obtained**by replacing the element aigby 1 and all the other elements of the ith row and jth column by 0 and calculating

the resulting determinant . Denoting the cofactor of aig by Ais , it may be seen ...

Page 387

among other things , that the Bohr compactification of a locally compact Abelian

group G may be

its discrete topology , and then taking the character group of this discrete group .

among other things , that the Bohr compactification of a locally compact Abelian

group G may be

**obtained**by taking the character group Ĝ of G , equipping Ĝ withits discrete topology , and then taking the character group of this discrete group .

Page 607

54 , 2 ] had

neighborhood of a pole . A special case of Theorem 1 . 9 is due to Weyr [ 1 ] , and

in full generality it was proved by Hensel [ 1 ] . In regard to Theorem 1 . 10 ,

Frobenius [ 3 ; p .

54 , 2 ] had

**obtained**expansions for the resolvent ( 21 - T ) - 1 in theneighborhood of a pole . A special case of Theorem 1 . 9 is due to Weyr [ 1 ] , and

in full generality it was proved by Hensel [ 1 ] . In regard to Theorem 1 . 10 ,

Frobenius [ 3 ; p .

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

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analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero