## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 35

Page 311

Theorem 5.1 shows that there is an

X) and bass, X'), which is determined by the equation woz, a u(E), E e X. Thus,

since B(S, 2) is equivalent to C(S), ba(S. X) is equivalent to rea(S1) (Theorem ...

Theorem 5.1 shows that there is an

**isometric isomorphism**a' -– a between B” (S.X) and bass, X'), which is determined by the equation woz, a u(E), E e X. Thus,

since B(S, 2) is equivalent to C(S), ba(S. X) is equivalent to rea(S1) (Theorem ...

Page 313

The correspondence U : ui -- us is an

(S1, 22). (c) If E1 is in 2, then v(ul, E1) = v(U(ul), E1) for all u, in bassi, 21). PRoof.

Recalling that t is an isomorphism of X onto 21, it is clear that the mapping T is ...

The correspondence U : ui -- us is an

**isometric isomorphism**of bassi, 21) onto ca(S1, 22). (c) If E1 is in 2, then v(ul, E1) = v(U(ul), E1) for all u, in bassi, 21). PRoof.

Recalling that t is an isomorphism of X onto 21, it is clear that the mapping T is ...

Page 337

Thus, bass, 2) is isometrically isomorphic with the closed subspace BVo(I) of all

fe BV(I) such that f(a+) = 0. If N is the one-dimensional ... Thus f <-- u, determines

an

...

Thus, bass, 2) is isometrically isomorphic with the closed subspace BVo(I) of all

fe BV(I) such that f(a+) = 0. If N is the one-dimensional ... Thus f <-- u, determines

an

**isometric isomorphism**between NBV(I) and rba (I, X). Using Theorem 9.9, we...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

### Other editions - View all

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero