## 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 yo 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 yo be a closed subspace spanned by x , and

...

Page 736

On a method of solution of the

SSSR ( N . S . ) 72 , 667 – 670 ( 1950 ) . ( Russian ) Math . Rev . 12 , 183 ( 1951 )

. Bari ( Bary ) , N . K . 1 . Biorthogonal systems and bases in Hilbert space .

On a method of solution of the

**equation**of heat conduction . Doklady Akad . NaukSSSR ( N . S . ) 72 , 667 – 670 ( 1950 ) . ( Russian ) Math . Rev . 12 , 183 ( 1951 )

. Bari ( Bary ) , N . K . 1 . Biorthogonal systems and bases in Hilbert space .

Page 780

Nelson Dunford, Jacob T. Schwartz. 3 . On the detection of the oscillation of a

second order linear differential

On self - adjoint differential

Nelson Dunford, Jacob T. Schwartz. 3 . On the detection of the oscillation of a

second order linear differential

**equation**. Duke Math . J . 17 , 57 - 62 ( 1950 ) . 4 .On self - adjoint differential

**equations**of second order . J . London Math . Soc .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

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