## Linear Operators: General theory |

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Page 169

5 Show that (i), (ii), and (iii) of Theorem 8.6 imply that / is in LV(S, Z, fi) and that |/„

— /|„ converges to

. Suppose that the field Z is separable under the metric q(E, F) = v(/j,, EA F).

5 Show that (i), (ii), and (iii) of Theorem 8.6 imply that / is in LV(S, Z, fi) and that |/„

— /|„ converges to

**zero**even if {/„} is a generalized sequence. 6 Let fi be bounded. Suppose that the field Z is separable under the metric q(E, F) = v(/j,, EA F).

Page 204

Since fi(Fn) = Js^/n^K^^) does not converge to

follows from the dominated convergence theorem (6.16) that there is a point in for

which /„(s2,) 's defined for all n and for which the sequence )} does not converge

to ...

Since fi(Fn) = Js^/n^K^^) does not converge to

**zero**and since 0 fn(sai) ^ 1 itfollows from the dominated convergence theorem (6.16) that there is a point in for

which /„(s2,) 's defined for all n and for which the sequence )} does not converge

to ...

Page 452

If A is a subset of X, and p is in A, then there exists a non-

functional tangent to A at p if and only if the cone B with vertex p generated by A

is not dense in X. Proof. If q 4 K, then, by 2.12 we can find a functional / and a real

...

If A is a subset of X, and p is in A, then there exists a non-

**zero**continuous linearfunctional tangent to A at p if and only if the cone B with vertex p generated by A

is not dense in X. Proof. If q 4 K, then, by 2.12 we can find a functional / and a real

...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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