## Linear Operators: General theory |

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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-group {

Tn\n ...

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-group {

Tn\n ...

Page 749

Uniformity in linear spaces. Trans. Amer. Math. Soc. 44, 305-856 (1938). 2. Direct

decompositions of Banach spaces. Bol. Soc. Mat. Mexicana 3, 1-12 (1946). 3. An

individual

Uniformity in linear spaces. Trans. Amer. Math. Soc. 44, 305-856 (1938). 2. Direct

decompositions of Banach spaces. Bol. Soc. Mat. Mexicana 3, 1-12 (1946). 3. An

individual

**ergodic theorem**for non-commutative transformations.Page 825

Mean

1938). 5.

1940). 6. An abstract treatment of the individual

.

Mean

**ergodic theorem**in Banach spaces. Proc. Imp. Acad. Tokyo 14, 292-294 (1938). 5.

**Ergodic theorems**of Birkhoff-Khintchine's type. Jap. J. Math. 17, 31-36 (1940). 6. An abstract treatment of the individual

**ergodic theorem**. Proc. Imp. Acad.

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations disjoint Doklady Akad Duke Math element ergodic theorem exists finite dimensional function defined Hausdorff space Hence Hilbert space homeomorphism ibid inequality integral Lebesgue Lebesgue measure Lemma linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc Proof properties proved real numbers reflexive Riesz Russian Sbornik N. S. scalar self-adjoint semi-group sequentially compact Show simple functions spectral Studia Math subset subspace Suppose theory topological space Trans uniformly Univ valued function Vber vector space weak topology weakly compact zero