## Linear Operators: General theory |

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Page 24

If x e X , there is a sequence of points an € A with an → X . Since { an } is a

Cauchy sequence , and f is

a Cauchy sequence . Since Y is complete , there is a point g ( x ) € Y with / ( an )

→ g ...

If x e X , there is a sequence of points an € A with an → X . Since { an } is a

Cauchy sequence , and f is

**uniformly**continuous , the sequence { f ( an ) } is alsoa Cauchy sequence . Since Y is complete , there is a point g ( x ) € Y with / ( an )

→ g ...

Page 145

A sequence of functions { { n } defined on S with values in X converges u -

{ n } converges

the ...

A sequence of functions { { n } defined on S with values in X converges u -

**uniformly**if for each ε > 0 there is a set EEE such that v ( u , E ) < ε and such that {{ n } converges

**uniformly**on S - E . The sequence { In } converges u -**uniformly**tothe ...

Page 360

which vanishes in a neighborhood of a point p the sequence ( S . ) ( x )

converges to zero

% En ( x , z ) dz SM , then the convergence of Snf for a given c . o . n . system is

localized if ...

which vanishes in a neighborhood of a point p the sequence ( S . ) ( x )

converges to zero

**uniformly**for x in some neighborhood of p . 21 Show that if | S% En ( x , z ) dz SM , then the convergence of Snf for a given c . o . n . system is

localized if ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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