## Linear Operators: General theory |

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Page 452

If K is a closed cone with vertex p in a real locally convex linear topological space

X, and K =yt X, then there exists a nonzero

K at p. If A is a subset of X, and p is in A, then there exists a non-zero ...

If K is a closed cone with vertex p in a real locally convex linear topological space

X, and K =yt X, then there exists a nonzero

**continuous linear**functional tangent toK at p. If A is a subset of X, and p is in A, then there exists a non-zero ...

Page 454

Let A be a compact convex subset of a locally convex

Let T : A -*□ A be

proper closed convex subset AjCA such that T(A1)CA1. Proof. We may suppose

that ...

Let A be a compact convex subset of a locally convex

**linear**topological space X-Let T : A -*□ A be

**continuous**. If K contains at least two points, there exists aproper closed convex subset AjCA such that T(A1)CA1. Proof. We may suppose

that ...

Page 513

By considering the sequence {A„} defined in Exercise 11, show that this mapping

is not

mapping which is

, ...

By considering the sequence {A„} defined in Exercise 11, show that this mapping

is not

**continuous**in the strong operator topology. 13 If U : f)* ->• X* is a**linear**mapping which is

**continuous**with the ?J topology in 'JJ* and the X topology in X*, ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact