## Linear Operators, Part 1 |

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Page 505

To complete the proof of the corollary it must be shown that for an arbitrary x in X

the function x * ( • ) w is u - measurable and

let x , be a fixed element of X and let Y , be a closed subspace spanned by x , and

...

To complete the proof of the corollary it must be shown that for an arbitrary x in X

the function x * ( • ) w is u - measurable and

**equation**( i ) holds . Consequently ,let x , be a fixed element of X and let Y , be a closed subspace spanned by x , and

...

Page 564

19 Find the most general solution of the differential

the matrix of Exercise 5 . The next ten exercises refer to the stability theory of

systems of n linear homogeneous differential

Here A ...

19 Find the most general solution of the differential

**equation**y ' = Ty where T isthe matrix of Exercise 5 . The next ten exercises refer to the stability theory of

systems of n linear homogeneous differential

**equations**, dy ( t ) / dt = A ( t ) y .Here A ...

Page 779

On the connection formulas and the solutions of the wave

51 , 669 - 676 ( 1937 ) . 2 . On the wave

Phys . Rev . 75 , 1573 - 1578 ( 1949 ) . 3 . The expansion problem in the theory of

...

On the connection formulas and the solutions of the wave

**equation**. Phys . Rev .51 , 669 - 676 ( 1937 ) . 2 . On the wave

**equation**with small quantum numbers .Phys . Rev . 75 , 1573 - 1578 ( 1949 ) . 3 . The expansion problem in the theory of

...

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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