## Linear Operators: General theory |

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Page 369

Consequently , unless xo ( t ) is a

most n + 1 points - 1 34 < tz . . . < tk < 1 , and there are

kicil = 1 , and in terms of which we may write an “ interpolation formula ” f ( a ) =

Cox ...

Consequently , unless xo ( t ) is a

**constant**of absolute value 1 , C is a set of atmost n + 1 points - 1 34 < tz . . . < tk < 1 , and there are

**constants**C , . . . , Cx withkicil = 1 , and in terms of which we may write an “ interpolation formula ” f ( a ) =

Cox ...

Page 516

42 Show that in Exercise 38 the set function u is unique up to a positive

factor if and only if n - 1 & n = 1 / ( $ ' ( s ) ) converges uniformly to a

each fe B ( S ) . 43 Show that in Exercise 39 the measure u is unique up to a ...

42 Show that in Exercise 38 the set function u is unique up to a positive

**constant**factor if and only if n - 1 & n = 1 / ( $ ' ( s ) ) converges uniformly to a

**constant**foreach fe B ( S ) . 43 Show that in Exercise 39 the measure u is unique up to a ...

Page 564

21 Consider the matrix differential equation de dt = A ( t ) Y where a solution is a

nxn complex valued matrix Y ( t ) , differentiable and satisfying the differential

equation for each tel . Show that for each to € I and each complex (

matrix ...

21 Consider the matrix differential equation de dt = A ( t ) Y where a solution is a

nxn complex valued matrix Y ( t ) , differentiable and satisfying the differential

equation for each tel . Show that for each to € I and each complex (

**constant**)matrix ...

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 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

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