## Linear Operators: General theory |

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Page 34

The binary operation u is often written as u ( a , b ) = ab , and , when this notation is used , it is

The binary operation u is often written as u ( a , b ) = ab , and , when this notation is used , it is

**called**multiplication . The element ab is**called**the ...Page 35

A mapping h : A + B between groups A and B is

A mapping h : A + B between groups A and B is

**called**a homomorphism if h ( ab ) = h ( a ) h ( b ) . A one - to - one homomorphism is**called**an isomorphism .Page 38

Since there is a one - to - one linear map between the spaces M ; and Xi , the space X is often

Since there is a one - to - one linear map between the spaces M ; and Xi , the space X is often

**called**the direct sum of the spaces X1 , ... , Xn . If M is ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed 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 function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero