## Linear operators: Spectral operators |

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Page 2144

M{T) in the

with T. Proof. Let A be the spectral measure in the adjoint space X* which is

associated with T* as in the preceding theorem. If X is weakly complete, ^4(8) is

the ...

M{T) in the

**strong operator topology**. This extension is bounded and commuteswith T. Proof. Let A be the spectral measure in the adjoint space X* which is

associated with T* as in the preceding theorem. If X is weakly complete, ^4(8) is

the ...

Page 2194

1.5) that a convex set in the space of all bounded linear maps between two 5-

spaces has the same closure in the weak as in the

Thus the strong and weak operator closures of an algebra of operators are the

same.

1.5) that a convex set in the space of all bounded linear maps between two 5-

spaces has the same closure in the weak as in the

**strong operator topology**.Thus the strong and weak operator closures of an algebra of operators are the

same.

Page 2204

Spectral operators Nelson Dunford, Jacob T. Schwartz. natural increasing order

of projections, it is seen from (iii) that xA(e)z* = lira x*Eax. a On the other hand, it

follows from Lemma 4 that Ea=\j Ett = Km.Ea a a in the

Spectral operators Nelson Dunford, Jacob T. Schwartz. natural increasing order

of projections, it is seen from (iii) that xA(e)z* = lira x*Eax. a On the other hand, it

follows from Lemma 4 that Ea=\j Ett = Km.Ea a a in the

**strong operator topology**.### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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