## 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 product ab is required to satisfy the following conditions : ( i ) a ( bc ) ...

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 conditions : ( i ) a ( bc ) ...

Page 35

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

= h ( a ) h ( b ) . A one - to - one homomorphism is

→ B is an isomorphism and if h ( A ) = B , then A and B are said to be ...

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 be ...

Page 38

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

space X is often

subspace of the vector space X over the field Ø , the factor space X / M is the set

of cosets of ...

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 X7 , . . . , Xn . If M is asubspace of the vector space X over the field Ø , the factor space X / M is the set

of cosets of ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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