## Linear Operators: General theory |

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Page 67

A closed linear manifold in a

closed linear manifold in the

equation $ ( w * ly = x * y , Y e Y . Clearly ( « * ) < æ * , so that & : X * → Y * . Let n :

y ...

A closed linear manifold in a

**reflexive**B - space is**reflexive**. Proof . Let y be aclosed linear manifold in the

**reflexive**space X . Let : x * →y * be defined by theequation $ ( w * ly = x * y , Y e Y . Clearly ( « * ) < æ * , so that & : X * → Y * . Let n :

y ...

Page 88

conjugate is isometric was proved by Hahn [ 3 ; p . 219 ] who was ... He used the

term regular to describe what we , following Lorch [ 2 ] , have called

**Reflexivity**. The fact that the natural isomorphism of a B - space X into its secondconjugate is isometric was proved by Hahn [ 3 ; p . 219 ] who was ... He used the

term regular to describe what we , following Lorch [ 2 ] , have called

**reflexive**.Page 425

Q . E . D . Theorems 2 and 5 lead to an important result on

THEOREM . A B - space is

in the weak topology . PROOF . Let X be a

Q . E . D . Theorems 2 and 5 lead to an important result on

**reflexive**spaces . 7THEOREM . A B - space is

**reflexive**if and only if its closed unit sphere is compactin the weak topology . PROOF . Let X be a

**reflexive**B - space , and let z be the ...### What people are saying - Write a review

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero