## Linear Operators: General theory |

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A linear

A linear

**vector**space , linear space , or**vector**space over a field 0 is an additive group X together with an operation m : x X → X , written as m ( a , x ) = ar , which satisfy the following four conditions : ( i ) a ( x + y ) = ax ...Page 250

For an arbitrary

For an arbitrary

**vector**ć in H the**vector**x- ( y * x ) / ( y * yı ) yı is in M so that ( x , y ) = y ** ( y1 , y ) / y * yı = y * x , which proves the existence of the desired y . To see that y is unique , let y ' be an element of H ...Page 795

Compact metric Boolean algebras and

Compact metric Boolean algebras and

**vector**lattices . J. Sci . Hirosima Univ . Ser . A. 11 , 125–128 ( 1942 ) . 2. On Fréchet lattices , I. J. Sci . Hirosima Univ . Ser . A. 12 , 235–248 ( 1943 ) . ( Japanese ) Math . Rev.### 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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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact operator complex Consequently contains converges convex Corollary 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 implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm obtained problem Proc projection PROOF properties proved range representation respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero