## Linear Operators, Part 1 |

### From inside the book

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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 aij by Aij , it may be seen that

...

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 aij by Aij , it may be seen that

...

Page 233

Nelson Dunford, Jacob T. Schwartz. Integrals for functions with values in a locally

convex topological space were

these integrals are countably additive integrals . In Section IV . 10 we will present

...

Nelson Dunford, Jacob T. Schwartz. Integrals for functions with values in a locally

convex topological space were

**obtained**by Phillips [ 7 ] and Rickart [ 1 ] . All ofthese integrals are countably additive integrals . In Section IV . 10 we will present

...

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 .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 other sections not shown

### 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

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero