## Linear Operators: General theory |

### From inside the book

Results 1-3 of 92

Page 20

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 olan , an ) = 0 . If everyCauchy

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

Page 68

The space X is said to be weakly complete if every weak Cauchy

weak limit . In Chapter V , a topology is introduced in certain linear spaces in

such a way that they become Hausdorff spaces in which the notion of

convergence ...

The space X is said to be weakly complete if every weak Cauchy

**sequence**has aweak limit . In Chapter V , a topology is introduced in certain linear spaces in

such a way that they become Hausdorff spaces in which the notion of

convergence ...

Page 345

Show that a

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

...

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

...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

10 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero