## Linear Operators: General theory |

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mutative topological group under addition , and if the mapping ( Q , x ) → Ox of ♡ XX into X is continuous . ... XG into G. ( b ) In a linear

mutative topological group under addition , and if the mapping ( Q , x ) → Ox of ♡ XX into X is continuous . ... XG into G. ( b ) In a linear

**topological space**X , all linear combinations of any number of scalars Qi , . , c.m. and ...Page 413

non - zero linear functional on the complex space X , which separates the sets M and N. Q.E.D. 2. Linear

non - zero linear functional on the complex space X , which separates the sets M and N. Q.E.D. 2. Linear

**Topological Spaces**In this section , the results of Section 1 are applied to linear**topological spaces**.Page 419

If I ' is a total linear space of linear functionals on X , X is a locally convex linear

If I ' is a total linear space of linear functionals on X , X is a locally convex linear

**topological space**in its r topology . Note that X may already be a linear**topological space**, possessing notions of open and closed subsets ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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