## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 78

Page 21

A set is said to be

nowhere

, if it contains a denumerable

A set is said to be

**dense**in a topological space A. if its closure is X. It is said to benowhere

**dense**if its closure does not contain any open set. A space is separable, if it contains a denumerable

**dense**set. 12 THEOREM. If a topological space ...Page 450

If a conver subset of a separable B-space & has an interior point, it has a unique

tangent at each point of a

convex set. It will be shown that –t(a, y) = r(x, -y), ye 3., for a in a

of ...

If a conver subset of a separable B-space & has an interior point, it has a unique

tangent at each point of a

**dense**subset of its boundary. PRoof. Let K be theconvex set. It will be shown that –t(a, y) = r(x, -y), ye 3., for a in a

**dense**subset Zof ...

Page 842

... III.4.11 (130) Lebesgue decomposition, III.4.14 (132) Saks decomposition, IV.

9.7 (30S) Yosida-Hewitt decomposition, (233) De Morgan, rules of, (2)

convex sets, V.7.27 (437)

set, ...

... III.4.11 (130) Lebesgue decomposition, III.4.14 (132) Saks decomposition, IV.

9.7 (30S) Yosida-Hewitt decomposition, (233) De Morgan, rules of, (2)

**Dense**convex sets, V.7.27 (437)

**Dense**linear manifolds, V.7.40–41 (438–439)**Dense**set, ...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero