## Linear Operators: General theory |

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Page 494

From IV. 10. 2 we conclude that T* maps the unit sphere of X* into a conditionally

weakly compact set of rca(S), and therefore T* is a weakly

Theorem 4.8 this implies that T is a weakly

From IV. 10. 2 we conclude that T* maps the unit sphere of X* into a conditionally

weakly compact set of rca(S), and therefore T* is a weakly

**compact operator**. ByTheorem 4.8 this implies that T is a weakly

**compact operator**. Q.E.D. 4 Theorem.Page 540

operator and the operator mapping into a weakly complete space X. Weakly

discussion of weakly

Grothendieck ...

operator and the operator mapping into a weakly complete space X. Weakly

**compact operators**from C[0, 1] to X were treated by Sirvint [8]. A very incisivediscussion of weakly

**compact operators**with domain C(S) was given byGrothendieck ...

Page 577

Spectral Theory of

exercises in Section VI. 9 that a number of linear operators of importance in

analysis either are compact, or have compact squares. The structure of the

spectrum of ...

Spectral Theory of

**Compact Operators**It has been observed in some of theexercises in Section VI. 9 that a number of linear operators of importance in

analysis either are compact, or have compact squares. The structure of the

spectrum of ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

44 other sections not shown

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Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma 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 properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero