## Linear Operators: General theory |

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Page 56

Since the map y -* ny is a

set V. Thus, TG 2 TM-TM 2 TM-TM □ F- V. Since a map of the form y -+ a—y is a

of ...

Since the map y -* ny is a

**homeomorphism**in ?), TM contains a non-void openset V. Thus, TG 2 TM-TM 2 TM-TM □ F- V. Since a map of the form y -+ a—y is a

**homeomorphism**, theseta^F is open. Since the set V—V = u (a— V) is the unionof ...

Page 91

However, Kolmogoroff [1] proved that a topological linear space is

there is an algebraic isomorphism which is also a

each of the spaces ...

However, Kolmogoroff [1] proved that a topological linear space is

**homeomorphic**to a normed linear space if and only if ... 182—4)] showed thatthere is an algebraic isomorphism which is also a

**homeomorphism**betweeneach of the spaces ...

Page 442

If Q is a compact Hausdorff space, and C(Q) is the B-space of all real or complex

continuous functions on Q, then the mapping X : q -> x* of Q into a subset Q of the

extremal points of S* is a

If Q is a compact Hausdorff space, and C(Q) is the B-space of all real or complex

continuous functions on Q, then the mapping X : q -> x* of Q into a subset Q of the

extremal points of S* is a

**homeomorphism**where C*(Q) has its C(Q) topology.### 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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additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations disjoint Doklady Akad Duke Math element ergodic theorem exists finite dimensional function defined Hausdorff space Hence Hilbert space homeomorphism ibid inequality integral Lebesgue Lebesgue measure Lemma linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc Proof properties proved real numbers reflexive Riesz Russian Sbornik N. S. scalar self-adjoint semi-group sequentially compact Show simple functions spectral Studia Math subset subspace Suppose theory topological space Trans uniformly Univ valued function Vber vector space weak topology weakly compact zero