## Linear Operators: General theory |

### From inside the book

Results 1-3 of 61

Page 505

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

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

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

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

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

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

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 763

On the essential spectra of ordinary differential

asymptotic arcus variation of solutions of real linear differential

second order . Amer . ... Criteria for the non - degeneracy of the wave

Amer .

On the essential spectra of ordinary differential

**equations**. Amer . ... Theasymptotic arcus variation of solutions of real linear differential

**equations**ofsecond order . Amer . ... Criteria for the non - degeneracy of the wave

**equation**.Amer .

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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