## Linear Operators: General theory |

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A

} in a metric space is a Cauchy

Cauchy

...

A

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

**sequence**if limm . n e ( am , an ) = 0 . If everyCauchy

**sequence**is convergent , a metric space is said to be complete . The next...

Page 68

which converges weakly to a point in X . Every

is a Cauchy

which converges weakly to a point in X . Every

**sequence**{ xn } such that { w * xn }is a Cauchy

**sequence**of scalars for each x * € X * is called a weak Cauchy**sequence**. The space X is said to be weakly complete if every weak Cauchy ...Page 345

Show that a

and converges at each point of the boundary of D ( to f ) . Show that a subset of A

( D ) ...

Show that a

**sequence**of functions in A ( D ) is a weak Cauchy**sequence**( a**sequence**converging weakly to f in A ( D ) ) if and only if it is uniformly boundedand converges at each point of the boundary of D ( to f ) . Show that a subset of A

( D ) ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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