## Linear Operators: General theory |

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Page 412

The

The

**linear functional**f separates the subsets M and X of X if and only if it separates the subsets M - N and { 0 } of X. The proof is elementary , and is left to the reader . In dealing with subspaces , it is often convenient to make ...Page 421

Let X be a linear space , and let I be a total subspace of X * . Then the

Let X be a linear space , and let I be a total subspace of X * . Then the

**linear functionals**on X which are continuous in the I topology are precisely the functionals in T. The proof of Theorem 9 will be based on the following lemma .Page 452

If K is a closed cone with vertex p in a real locally convex linear topological space X , and K + X , then there exists a nonzero continuous

If K is a closed cone with vertex p in a real locally convex linear topological space X , and K + X , then there exists a nonzero continuous

**linear functional**tangent to K at p . If A is a subset of X , and р is in A , then there exists ...### 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