## Linear Operators: General theory |

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Page 462

116 ] . Dieudonné [ 3 ; p . 109 ] proved 3 . 9 after establishing Lemma 3 . 10 by

induction . The case of Theorem 3 . 9 in which X = Y * and I ' = Y , was proved in

the separable case by

116 ] . Dieudonné [ 3 ; p . 109 ] proved 3 . 9 after establishing Lemma 3 . 10 by

induction . The case of Theorem 3 . 9 in which X = Y * and I ' = Y , was proved in

the separable case by

**Banach**[ 1 ; p . 131 ] and in full generality by Alaoglu 1 ; p .Page 802

The singular elements of a

1947 ) . 5 . Isomorphic groups of linear transformations . Amer . J . Math . 72 , 451

- 464 ( 1950 ) . 6 .

The singular elements of a

**Banach**algebra . Duke Math . J . 14 , 1063 - 1077 (1947 ) . 5 . Isomorphic groups of linear transformations . Amer . J . Math . 72 , 451

- 464 ( 1950 ) . 6 .

**Banach**algebras with an adjoint operation . Ann . of Math .Page 804

On a class of Markoff processes . Trans . Amer . Math . Soc . 71 , 120 - 135 ( 1951

) . Rosenbloom , P . C . 1 . Elements of mathematical logic . Dover Publications ,

New York , 1950 . 2 . Perturbations of linear operators in

On a class of Markoff processes . Trans . Amer . Math . Soc . 71 , 120 - 135 ( 1951

) . Rosenbloom , P . C . 1 . Elements of mathematical logic . Dover Publications ,

New York , 1950 . 2 . Perturbations of linear operators in

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero