## Linear Operators: General theory |

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Page 50

2 Lemma, (a) In a topological group G, any algebraic combination of any number

of variables xv . . n xn is continuous as a map of Gx. . . xG into G. (b) In a

„ ...

2 Lemma, (a) In a topological group G, any algebraic combination of any number

of variables xv . . n xn is continuous as a map of Gx. . . xG into G. (b) In a

**linear****topological space**X, all linear combinations of any number of scalar s ocj, . . ., <x„„ ...

Page 413

non-zero linear functional on the complex space X, which separates the sets M

and N. Q.E.D. 2.

1 are applied to

non-zero linear functional on the complex space X, which separates the sets M

and N. Q.E.D. 2.

**Linear Topological Spaces**In this section, the results of Section1 are applied to

**linear topological spaces**. Statements 1—6 of this section are ...Page 419

Let X be a

, e) = {q\\nP)-f(q)\ < e, f e A}, where p e X, lAj is a_finite subset_of. £Land e > 0.

Let X be a

**linear**vector**space**, and let r be a total subspace of X+. Then the T**topology**of X is the**topology**obtained by taking as base all sets of the form N(p; A, e) = {q\\nP)-f(q)\ < e, f e A}, where p e X, lAj is a_finite subset_of. £Land e > 0.

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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