## Linear Operators: General theory |

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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 * ( • ) x 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 * ( • ) x 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 762

On a class of linear

The Lg - solutions of linear differential

logarithmico - exponential differential

On a class of linear

**equations**with symmetrizable operators . Doklady Akad . ...The Lg - solutions of linear differential

**equations**of second order . ... On the linearlogarithmico - exponential differential

**equation**of the second order . Amer .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 .

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero