## Linear Operators: General theory |

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The space bs is the linear space of all sequences x = { an } of

The space bs is the linear space of all sequences x = { an } of

**scalars**for which the norm n | oc | sup Σα , 72 is ... ( s ) SES A**scalar**function f on S is E - measurable if | - | ( A ) e £ for every Borel set A in the range of f .Page 256

If , however , each of the spaces X , ... , Xn are Hilbert spaces then it will always be understood , sometimes without explicit mention , that X is the uniquely determined Hilbert space with

If , however , each of the spaces X , ... , Xn are Hilbert spaces then it will always be understood , sometimes without explicit mention , that X is the uniquely determined Hilbert space with

**scalar**product n ( iv ) ( [ 27 , ... , Xn ] ...Page 323

A

A

**scalar**valued measurable function f is said to be integrable if there exists a sequence { n } of simple functions such that ( i ) In ( s ) converges to f ( s ) u - almost everywhere ; ( ii ) the sequence { Setu ...### 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