## Linear Operators: General theory |

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Page 26

Hence the

. Convergence and Uniform Convergence of Generalized Sequences The notion

of convergence introduced in Definition 6 . 5 is not sufficiently general for all our ...

Hence the

**identity**is a homeomorphism and the space is metrizable . Q . E . D . 7. Convergence and Uniform Convergence of Generalized Sequences The notion

of convergence introduced in Definition 6 . 5 is not sufficiently general for all our ...

Page 249

Nelson Dunford, Jacob T. Schwartz, William G. Bade. PROOF . The

y2 + x - y ) 2 = 2 x2 +2 \ y ?, X , YEH , called the parallelogram

immediately from the axioms . If 8 = inf x - k | the preceding

keK ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade. PROOF . The

**identity**( x +y2 + x - y ) 2 = 2 x2 +2 \ y ?, X , YEH , called the parallelogram

**identity**, followsimmediately from the axioms . If 8 = inf x - k | the preceding

**identity**shows thatkeK ...

Page 479

... and only if its adjoint T * has a bounded inverse ( T * ) - 1 defined on all of X * .

When these inverses exist , ( T - 1 ) * = ( T * ) - 1 PROOF . If T - l exists and is in B (

Y , X ) , then , by Lemma 4 , ( TT - 1 ) * = ( T - 1 ) * T * is the

... and only if its adjoint T * has a bounded inverse ( T * ) - 1 defined on all of X * .

When these inverses exist , ( T - 1 ) * = ( T * ) - 1 PROOF . If T - l exists and is in B (

Y , X ) , then , by Lemma 4 , ( TT - 1 ) * = ( T - 1 ) * T * is the

**identity**in Y * and ( T ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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