## Linear Operators: General theory |

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Page 37

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

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 494

It is clear that the operator T , defined by ( b ) , is a bounded

S ) to X whose adjoint T * is given by ( d ) . From IV . 10 . 2 we conclude that T *

maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) ...

It is clear that the operator T , defined by ( b ) , is a bounded

**linear operator**on C (S ) to X whose adjoint T * is given by ( d ) . From IV . 10 . 2 we conclude that T *

maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) ...

Page 513

13 If U : Y * → X * is a linear mapping which is continuous with the y topology in Y

* and the X topology in X * , then there exists a bounded

such that T * = U . 14 Let T be a linear , but not necessarily continuous ...

13 If U : Y * → X * is a linear mapping which is continuous with the y topology in Y

* and the X topology in X * , then there exists a bounded

**linear operator**T : X + Ysuch that T * = U . 14 Let T be a linear , but not necessarily continuous ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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