## Linear Operators: General theory |

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Page 494

From IV. 10.2 we conclude that T* maps the unit sphere of 36* 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 36* 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 539

operator and its importance was clearly recognized by E. Schmidt [1], to whom

the geometrical terminology in linear space theory is due. Compact and weakly

operator ...

operator and its importance was clearly recognized by E. Schmidt [1], to whom

the geometrical terminology in linear space theory is due. Compact and weakly

**compact operators**. The concept of a compact (or completely continuous)operator ...

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 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