## Linear Operators: General theory |

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Page 747

Operations in

Operations in

**Banach spaces**. Trans . Amer . Math . Soc . 51 , 583-608 ( 1942 ) . 10. Ergodic theorems for abelian semi - groups . Trans . Amer . Math . Soc . 51 , 399–412 ( 1942 ) . 11. Strict convexity and smoothness of normed spaces ...Page 810

Weak compactness in

Weak compactness in

**Banach spaces**. Studia Math . 11 , 71-94 ( 1950 ) . Skorohod , A. ( see Kostyučenko , A. ) Slobodyanskiĩ , M. G. 1. On estimates for the eigenvalues of a self - adjoint operator . Akad . Nauk SSSR . Prikl . Mat .Page 815

On linear equations in Hilbert space . Mat . Sbornik N. S. 29 ( 71 ) , 529-550 ... On the compactness of the space Lg . Bull . Amer . Math . Soc . ... On certain

On linear equations in Hilbert space . Mat . Sbornik N. S. 29 ( 71 ) , 529-550 ... On the compactness of the space Lg . Bull . Amer . Math . Soc . ... On certain

**Banach spaces**whose elements are analytic functions . Actas Acad . Ci .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

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