## 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 product of a and b . The product ab is required to satisfy the following ...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 . If h : A → B is an isomorphism and if h ( A ) = B , then A and B are said to ...Page 38

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

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

**called**the direct sum of the spaces X1 , . . . , Xn . If M is a subspace of the vector space X over the field Ø , the factor space X / M is ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero