## 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 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 X , Xno If M is a subspace of the vector space X over the field Ø , the factor space X / M is the set of ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero