## Linear Operators: General theory |

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Page 77

mn-V»+l)l < °°- M m=0 The transformation preserves sums of series (i.e. 2m-o (2n

=o^mnfln) = 2n=oa») if and only if the equation (1') 2m4»» = 1 holds for each n, ...

**converges**f°r every n; (2) 2n'^«»-^.,n+il**converges**for each m; M (3) SUp2„ 12 (^mn-V»+l)l < °°- M m=0 The transformation preserves sums of series (i.e. 2m-o (2n

=o^mnfln) = 2n=oa») if and only if the equation (1') 2m4»» = 1 holds for each n, ...

Page 145

A sequence of functions {/„} defined on S with values in X

if for each e > 0 there is a set E e E such that v(fi, E) < e and such that {/„}

function f ...

A sequence of functions {/„} defined on S with values in X

**converges**fx-uniformlyif for each e > 0 there is a set E e E such that v(fi, E) < e and such that {/„}

**converges**uniformly on S — E. The sequence {/„}**converges**fi-uniformly to thefunction f ...

Page 281

Let A be a dense subset of a compact Hausdorff space S, and suppose that a

sequence {/„} of continuous functions

continuous limit /„. Then {/„}

and every ...

Let A be a dense subset of a compact Hausdorff space S, and suppose that a

sequence {/„} of continuous functions

**converges**at every point of A to acontinuous limit /„. Then {/„}

**converges**to f0 at every point of S if and only if {/„}and every ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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