## Linear Operators: General theory |

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14

with 10 * 1 = 1 and x * x = læl . PROOF . Apply Lemma 12 with Y = 0 . The æ *

required in the present

...

14

**COROLLARY**. For every x + 0 in a normed linear space X , there is an a * • X *with 10 * 1 = 1 and x * x = læl . PROOF . Apply Lemma 12 with Y = 0 . The æ *

required in the present

**corollary**may then be defined as lx | times the æ * whose...

Page 188

Q . E . D . As in the case of finite measure spaces we shall call the measure

space ( S , E , u ) constructed in

, Eipi ) the product measure space and write ( S , E , u ) = P = 1 ( Si , Ei , Mi ) .

Q . E . D . As in the case of finite measure spaces we shall call the measure

space ( S , E , u ) constructed in

**Corollary**6 from the o - finite measure spaces ( Si, Eipi ) the product measure space and write ( S , E , u ) = P = 1 ( Si , Ei , Mi ) .

Page 662

Nelson Dunford, Jacob T. Schwartz. 2

lim , A ( n ) exists it is a projection of X upon the manifold { x | Tx = x } of fixed

points of T . The complementary projection has the closure of ( I – T ) X for its

range .

Nelson Dunford, Jacob T. Schwartz. 2

**COROLLARY**. When the strong limit E =lim , A ( n ) exists it is a projection of X upon the manifold { x | Tx = x } of fixed

points of T . The complementary projection has the closure of ( I – T ) X for its

range .

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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