## 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 : 0 X → X , written as m ( a , x ) = ax , which satisfy the following four conditions : ( i ) a ( x + y ) = aut + ...Page 250

If y * # 0 the set M = { wy * x = 0 } is a proper closed linear manifold in H and its orthocomplement N contains , by Lemma 4 , a

If y * # 0 the set M = { wy * x = 0 } is a proper closed linear manifold in H and its orthocomplement N contains , by Lemma 4 , a

**vector**41 + 0. Let y = ayı where a = y * ( y ) / | y1 | 2 . For an arbitrary**vector**x in H the**vector**x- ...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 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen 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