## 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 | 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