## Linear Operators: General theory |

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Page 475

CHAPTER VI

linear maps between B- spaces begun in Chapter II. Various

introduced in the space B(H, ?)) of bounded linear maps between the B-spaccs X

, and ...

CHAPTER VI

**Operators**and Their Adjoints This chapter continues the study oflinear maps between B- spaces begun in Chapter II. Various

**topologies**areintroduced in the space B(H, ?)) of bounded linear maps between the B-spaccs X

, and ...

Page 511

is algebraically isomorphic to a subspacc of the product P&z SQX, where S£)x =

3), under the mapping T -* PM£ Tx. Show that the strong

B(X, 3)) is identical with the usual product

is algebraically isomorphic to a subspacc of the product P&z SQX, where S£)x =

3), under the mapping T -* PM£ Tx. Show that the strong

**topology**of**operators**inB(X, 3)) is identical with the usual product

**topology**where the strong**topology**is ...Page 512

is also separable, A is sequentially compact in the weak

only if A is compact in the weak

closed unit sphere of "2) ) is compact in the weak

is also separable, A is sequentially compact in the weak

**operator topology**if andonly if A is compact in the weak

**operator topology**. 6 If ?) is reflexive, then theclosed unit sphere of "2) ) is compact in the weak

**operator topology**. Conversely ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

a-finite 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 continuous linear functional convex set Corollary countably additive Definition denote dense Doklady Akad element equivalent everywhere exists finite dimensional follows from Theorem function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative non-zero normed linear space 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 valued function vector space weak topology weakly compact weakly sequentially compact zero