## Linear Operators, Part 1 |

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Page 729

Theorems for abstract vector lattices were proved by G . Birkhoff [ 2 ] , Kakutani [ 7

, 8 ] , and F . Riesz [ 17 ] . Several generalizations of the mean

groups or semi - groups of operators more general than the discrete semi ...

Theorems for abstract vector lattices were proved by G . Birkhoff [ 2 ] , Kakutani [ 7

, 8 ] , and F . Riesz [ 17 ] . Several generalizations of the mean

**ergodic theorem**togroups or semi - groups of operators more general than the discrete semi ...

Page 749

An individual

Math . Szeged 14 , 1 - 4 ( 1951 ) . 4 . Integration in general analysis . Trans . Amer

. Math . Soc . 37 , 441 - 453 ( 1935 ) . On continuous mappings . Ann . of Math .

An individual

**ergodic theorem**for non - commutative transformations . Acta Sci .Math . Szeged 14 , 1 - 4 ( 1951 ) . 4 . Integration in general analysis . Trans . Amer

. Math . Soc . 37 , 441 - 453 ( 1935 ) . On continuous mappings . Ann . of Math .

Page 770

Mean

121 - 123 ( 1939 ) . 8 . Concrete representation of abstract ( L ) - spaces and the

mean

Mean

**ergodic theorems**in abstract ( L ) - spaces . Proc . Imp . Acad . Tokyo 15 ,121 - 123 ( 1939 ) . 8 . Concrete representation of abstract ( L ) - spaces and the

mean

**ergodic theorem**. Ann . of Math . ( 2 ) 42 , 523 - 537 ( 1941 ) . 9 . Concrete ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

25 other sections not shown

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### Common terms and phrases

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