## Linear Operators, Part 1 |

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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...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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