## Linear Operators: General theory |

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A sequence {an} is said to be convergent if an a for some a. A sequence {a„} in a

metric space is a

lemmas ...

A sequence {an} is said to be convergent if an a for some a. A sequence {a„} in a

metric space is a

**Cauchy sequence**if limm o(am, a„) = 0. If every**Cauchy****sequence**is convergent, a metric space is said to be complete. The next threelemmas ...

Page 68

which converges weakly to a point in X. Every sequence {xn} such that {x*xn} is a

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

which converges weakly to a point in X. Every sequence {xn} such that {x*xn} is a

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

**Cauchy sequence**has ...Page 122

Let 1 i£j p < oo; let {/„} be a sequence of functions in L„(S, E, fi,£) and let f be a

function on S to X. Then f is in Lv and ... Thus to see that the sequence {g„} is a

EJ.

Let 1 i£j p < oo; let {/„} be a sequence of functions in L„(S, E, fi,£) and let f be a

function on S to X. Then f is in Lv and ... Thus to see that the sequence {g„} is a

**Cauchy sequence**in L^S) it will suffice to prove that it is a**Cauchy sequence**in L^EJ.

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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