## Linear Operators, Part 1 |

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Page 554

It is clear that the closed subspace 30 C & has the property that every

there is a projection (of norm 1) from 3: onto 3.0. Thus Kakutani [6] proved that 3:

...

It is clear that the closed subspace 30 C & has the property that every

**bounded****operator**T : 30 – 9)r has an extension (with the same norm) T : 3 - ?), if and only ifthere is a projection (of norm 1) from 3: onto 3.0. Thus Kakutani [6] proved that 3:

...

Page 600

But, in contrast to the case where T is a

a bounded set, an unbounded set, the void set, or even the whole plane. This is

observed in Exercise 10.1. We exclude the last possibility, and suppose ...

But, in contrast to the case where T is a

**bounded operator**, the spectrum may bea bounded set, an unbounded set, the void set, or even the whole plane. This is

observed in Exercise 10.1. We exclude the last possibility, and suppose ...

Page 641

In this section we suppose A is the infinitesimal generator of a strongly

continuous group of operators T(t), – o – t < 00, and show in this case how

class will include ...

In this section we suppose A is the infinitesimal generator of a strongly

continuous group of operators T(t), – o – t < 00, and show in this case how

**bounded operators**may be assigned to each of a larger class of functions. Thisclass will include ...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero