## Linear Operators: General theory |

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Results 1-3 of 93

Page 239

The space I " . is the

scalars dy , . . . , Chon with the norm lx | = sup laila 1 Sisn 4 . The space lo is

defined for 1 p < oo as the

which ...

The space I " . is the

**linear space**of all ordered n - tuples x = [ 0 , . . . , Cen ] ofscalars dy , . . . , Chon with the norm lx | = sup laila 1 Sisn 4 . The space lo is

defined for 1 p < oo as the

**linear space**of all sequences x = { en } of scalars forwhich ...

Page 410

The intersection of an arbitrary family of convex subsets of the

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 x„ be points in the

convex ...

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 x„ be points in the

convex ...

Page 838

space of, definition, IV.2.24 (242) properties, IV.15 Annihilator of a set, II.4.17 (72)

Arzela theorem, on continuity of limit ... for compactness with, IV.5.5 (260)

definition, II.4.7 (71) properties, II.4.8-12 (71) remarks on, (93-94) in a

space of, definition, IV.2.24 (242) properties, IV.15 Annihilator of a set, II.4.17 (72)

Arzela theorem, on continuity of limit ... for compactness with, IV.5.5 (260)

definition, II.4.7 (71) properties, II.4.8-12 (71) remarks on, (93-94) in a

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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 spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero