## Linear Operators, Part 1 |

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Page 495

Since 980 is an algebra and

field contained in Ø. We now show that Øo = % by proving that Øo contains all the

closed sets. Let F be an arbitrary closed set in S. Since S is assumed to be a ...

Since 980 is an algebra and

**satisfies**condition (ii), it is readily seen that % is a g-field contained in Ø. We now show that Øo = % by proving that Øo contains all the

closed sets. Let F be an arbitrary closed set in S. Since S is assumed to be a ...

Page 498

The norm of T

Conversely, if a.”(-) on X to 3°

(S, 2, u) whose norm

a ...

The norm of T

**satisfies**the relations (iii) sup w”(E) < |T| < 4 sup w”(E). Ee 2. EelConversely, if a.”(-) on X to 3°

**satisfies**(i) then (ii) defines an operator T on 3 to L1(S, 2, u) whose norm

**satisfies**(iii). Furthermore T is weakly compact if and only ifa ...

Page 557

If A, 40(T), then (T-A,I), = 0 implies a = 0. Consequently, the product R, of all the

factors (2–2,)” in R such that 2, e o (T), still

the product R., of all the factors (2–2,)”, where p, — min (x, y(A)),

0.

If A, 40(T), then (T-A,I), = 0 implies a = 0. Consequently, the product R, of all the

factors (2–2,)” in R such that 2, e o (T), still

**satisfies**R1(T) = 0. In the same way,the product R., of all the factors (2–2,)”, where p, — min (x, y(A)),

**satisfies**R2(T) =0.

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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