## Linear Operators: General theory |

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Page 58

Hence, by Theorem 2, its inverse pr^1 is

each of two metrics, and if one of the corresponding topologies contains the other

, the two ...

Hence, by Theorem 2, its inverse pr^1 is

**continuous**. Thus T = PrmPr^ is**continuous**(1.4.17). Q.E.D. 5 Theorem. If a**linear**space is an F-space undereach of two metrics, and if one of the corresponding topologies contains the other

, the two ...

Page 452

If A is a subset of X, and p is in A, then there exists a non-zero

functional tangent to A at p if and only if the cone B with vertex p generated by A

is not dense in X. Proof. If q 4 K, then, by 2.12 we can find a functional / and a real

...

If A is a subset of X, and p is in A, then there exists a non-zero

**continuous linear**functional tangent to A at p if and only if the cone B with vertex p generated by A

is not dense in X. Proof. If q 4 K, then, by 2.12 we can find a functional / and a real

...

Page 513

By considering the sequence {An} defined in Exercise 11, show that this mapping

is not

mapping which is

...

By considering the sequence {An} defined in Exercise 11, show that this mapping

is not

**continuous**in the strong operator topology. 13 If 17 : ?)* -*□ X* is a**linear**mapping which is

**continuous**with the 2) topology in ?)* and the X topology in X*...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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