## Linear Operators, Part 1 |

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A

a metric space is a Cauchy

A

**sequence**{an} is said to be convergent if an -- a for some a. A**sequence**{an} ina metric space is a Cauchy

**sequence**if limo., Q(a, , a,) = 0. If every Cauchy**sequence**is convergent, a metric space is said to be complete. The next three ...Page 68

Every

e 3." is called a weak Cauchy

complete if every weak Cauchy

topology is ...

Every

**sequence**{a,} such that {r+a,} is a Cauchy**sequence**of scalars for each a'e 3." is called a weak Cauchy

**sequence**. The space 3 is said to be weaklycomplete if every weak Cauchy

**sequence**has a weak limit. In Chapter V, atopology is ...

Page 345

37 Let D be a bounded domain. Show that a

weak Cauchy

it is uniformly bounded and converges at each point of the boundary of D (to f).

37 Let D be a bounded domain. Show that a

**sequence**of functions in A (D) is aweak Cauchy

**sequence**(a**sequence**converging weakly to fin A(D)) if and only ifit is uniformly bounded and converges at each point of the boundary of D (to f).

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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