## Linear Operators: General theory |

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Page 462

The case of Theorem 3.9 in which X Y * and I Y , was proved in the separable

case by

Michael [ 1 ] gave an extension of Lemma 3.10 to a case where linear operators

are ...

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 . 256 ] .Michael [ 1 ] gave an extension of Lemma 3.10 to a case where linear operators

are ...

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

Perturbations of linear operators in

1955 ) . Rosenthal , A. ( see Hahn , H. , and Hartogs , F. ) Rosser , J. B. 1. Logic

for mathematicians . McGraw - Hill Co. , New York , 1953 . Rota , G. C. 1.

Extension ...

Perturbations of linear operators in

**Banach**spaces . Arch . Math . 6 , 89–101 (1955 ) . Rosenthal , A. ( see Hahn , H. , and Hartogs , F. ) Rosser , J. B. 1. Logic

for mathematicians . McGraw - Hill Co. , New York , 1953 . Rota , G. C. 1.

Extension ...

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element 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 meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero