## Linear Operators: General theory |

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Page 311

Consider the closed subspace B(S, E) of B(S). According to Theorems 6.18 and

6.20 there is a compact Hausdorff space St such that B(S, E) is equivalent to C(

5X). Theorem 5.1 shows that there is an

between ...

Consider the closed subspace B(S, E) of B(S). According to Theorems 6.18 and

6.20 there is a compact Hausdorff space St such that B(S, E) is equivalent to C(

5X). Theorem 5.1 shows that there is an

**isometric isomorphism**x* •< — * fibetween ...

Page 313

The correspondence U : fa -> fa is an

Sv E2). (c) // E1 is in Ex tfien v{fa, Et) = v(U(fa), Er) for all fa in ba(SvEl). Proof.

Recalling that t is an isomorphism of E onto Ev it is clear that the mapping T is an

...

The correspondence U : fa -> fa is an

**isometric isomorphism**of ba(Sv EJ onto ca(Sv E2). (c) // E1 is in Ex tfien v{fa, Et) = v(U(fa), Er) for all fa in ba(SvEl). Proof.

Recalling that t is an isomorphism of E onto Ev it is clear that the mapping T is an

...

Page 337

Thus, ba(S, E) is isometrically isomorphic with the closed subspace BV0(I) of all /

e BV(I) such that/(a + ) = 0. If N is the ... Thus / •« — *□ fif determines an

Thus, ba(S, E) is isometrically isomorphic with the closed subspace BV0(I) of all /

e BV(I) such that/(a + ) = 0. If N is the ... Thus / •« — *□ fif determines an

**isometric****isomorphism**between NBV(I) and rba(I, E). Using Theorem 9.9, we obtain the ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

44 other sections not shown

### 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

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