## Linear Operators: General theory |

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Page 104

Moreover, just as in the general case for a factor space (see Section 1.11) the

addition and scalar multiplication of equivalence classes is well defined. It is

customary to speak of the elements

than ...

Moreover, just as in the general case for a factor space (see Section 1.11) the

addition and scalar multiplication of equivalence classes is well defined. It is

customary to speak of the elements

**of F**(S, E, fi, X) as if they were functions ratherthan ...

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 | 34 |

Copyright | |

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### Common terms and phrases

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero