## Linear Operators, Part 1 |

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Page vi

The

mathematician . Much of the text has grown directly out of lectures given by the

authors over many years , and the two parts are designed to form suitable texts

for a variety of ...

The

**present**work is written for the student as well as for the maturemathematician . Much of the text has grown directly out of lectures given by the

authors over many years , and the two parts are designed to form suitable texts

for a variety of ...

Page 286

Nelson Dunford, Jacob T. Schwartz. 1 U - 1 Ei XE . discussion of the

section covers the space lo as well as the space L , ( S , E , u ) . THEOREM . If 1 <

p < oo and 1 / p + 1 / 9 = 1 , there is an isometric isomorphism between L * ( S , E ,

u ) ...

Nelson Dunford, Jacob T. Schwartz. 1 U - 1 Ei XE . discussion of the

**present**section covers the space lo as well as the space L , ( S , E , u ) . THEOREM . If 1 <

p < oo and 1 / p + 1 / 9 = 1 , there is an isometric isomorphism between L * ( S , E ,

u ) ...

Page 660

In the

space X will be given which are necessary and sufficient for the convergence in X

of the averages 1 A ( n ) = Σ Tm n - 1 n m = 0 of the iterates of T. These general ...

In the

**present**section conditions on an operator T in an arbitrary complex B -space X will be given which are necessary and sufficient for the convergence in X

of the averages 1 A ( n ) = Σ Tm n - 1 n m = 0 of the iterates of T. These general ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Common terms and phrases

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