## 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 ^ X, then there exists a nonzero

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

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

X, and K ^ X, then there exists a nonzero

**continuous linear**junctional tangent to Kat p. If A is a subset of X, and p is in A, then there exists a non-zero continuous ...

Page 454

Let A be a compact co-nvex subset of a locally convex

Let T : A -»□ A be

proper closed convex subset AXCA such that TiK^QKi. Proof. We may suppose

that ...

Let A be a compact co-nvex subset of a locally convex

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

**continuous**. If A contains at least two points, there exists aproper closed convex subset AXCA such that TiK^QKi. 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 : 9)* -> X* is a**linear**mapping which is

**continuous**with the 9) topology in 9J* 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 closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function 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 Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero