## Linear Operators: General theory |

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If X , Y , Z are topological spaces , and it f : X → Y and g : Y + Z are

If X , Y , Z are topological spaces , and it f : X → Y and g : Y + Z are

**continuous**, then the composite**function**g is**continuOus**.Page 274

... of all complex

... of all complex

**continuous functions**on S. Let A be a closed subalgebra of C ... To prove the converse , let A , consist of the real functions in A. Then ...Page 381

10 ] , Hewitt [ 3 ] and Edwards [ 1 ] consider functionals on the space of

10 ] , Hewitt [ 3 ] and Edwards [ 1 ] consider functionals on the space of

**continuous functions**on a locally compact Hausdorff space which vanish outside of ...### 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