## Linear Operators: General theory |

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Page 36

is commutative if the identity ab = ba is valid . A field is a commutative ring in

which the non - zero elements form a group under multiplication . The unit of this

group in a field will be written as 1 instead of e . A

space ...

is commutative if the identity ab = ba is valid . A field is a commutative ring in

which the non - zero elements form a group under multiplication . The unit of this

group in a field will be written as 1 instead of e . A

**linear**vector space ,**linear**space ...

Page 37

If T : X + Y and U : Y → Z are

spaces over the same field Ø , the product UT , defined by ( UT ) x = U ( Tx ) , is a

said ...

If T : X + Y and U : Y → Z are

**linear**transformations , and X , Y , Z are**linear**spaces over the same field Ø , the product UT , defined by ( UT ) x = U ( Tx ) , is a

**linear**transformation which maps X into Z . If T is a**linear**operator on X to X , it issaid ...

Page 50

XG into G . ( b ) In a

number of scalars Oz , . . . , Olom : and vectors x , . . . , Xn , are continuous

mappings of ♡ X . . . X XX X . . . XX into X . ( c ) In a

group G ) ...

XG into G . ( b ) In a

**linear**topological space X , all**linear**combinations of anynumber of scalars Oz , . . . , Olom : and vectors x , . . . , Xn , are continuous

mappings of ♡ X . . . X XX X . . . XX into X . ( c ) In a

**linear**topological space X (group G ) ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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