## Linear Operators: General theory |

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Page 406

Cameron and Martin 2 , Cameron and Hatfield [ 1 ] , [ 2 ] establish a complete

orthonormal set of " Fourier - Hermite functionals ” in L ( C , EX Mw ) , and study

the theory of expansion of

functionals .

Cameron and Martin 2 , Cameron and Hatfield [ 1 ] , [ 2 ] establish a complete

orthonormal set of " Fourier - Hermite functionals ” in L ( C , EX Mw ) , and study

the theory of expansion of

**arbitrary**elements of L / ( Ĉ , Ew Mw ) in thesefunctionals .

Page 410

The intersection of an

convex . As examples of convex subsets of X , we note the subspaces of X , and

the subsets of X consisting of one point . 3 LEMMA . Let x1 , . . . , Xn be points in ...

The intersection of an

**arbitrary**family of convex subsets of the linear space X isconvex . As examples of convex subsets of X , we note the subspaces of X , and

the subsets of X consisting of one point . 3 LEMMA . Let x1 , . . . , Xn be points in ...

Page 476

... where A is an

strong topology , a generalized sequence { Ta } converges to T if and only if ( Txx

} converges to Tx for every x in X. 3 DEFINITION . The weak operator topology in

B ...

... where A is an

**arbitrary**finite subset of X , and ε > 0 is**arbitrary**. Thus , in thestrong topology , a generalized sequence { Ta } converges to T if and only if ( Txx

} converges to Tx for every x in X. 3 DEFINITION . The weak operator topology in

B ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero