## Linear Operators: General theory |

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Page 104

m+[g] = u+g]i «[/] = [a/]; \m\ = Since |g| = |/| if [g] = [

equation defines the norm uniquely. Moreover, just as in the general case for a

factor space (see Section 1. 11) the addition and scalar multiplication

equivalence ...

m+[g] = u+g]i «[/] = [a/]; \m\ = Since |g| = |/| if [g] = [

**f**]. it is clear that the aboveequation defines the norm uniquely. Moreover, just as in the general case for a

factor space (see Section 1. 11) the addition and scalar multiplication

**of**equivalence ...

Page 196

Next we study the relation between the theory

theory

integrals to concrete problems such as the representation

Next we study the relation between the theory

**of**product measures and thetheory

**of**vector valued integrals. In the application**of**the theory**of**vector valuedintegrals to concrete problems such as the representation

**of**operators between ...Page 412

The linear

separates the subsets M—N and {0} of X. The proof is elementary, and is left to

the reader. In dealing with subspaces, it is often convenient to make use of the

following ...

The linear

**functional f**separates the subsets M and N of X if and only if itseparates the subsets M—N and {0} of X. The proof is elementary, and is left to

the reader. In dealing with subspaces, it is often convenient to make use of the

following ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

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Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero