## Linear Operators: General theory |

### From inside the book

Results 1-3 of 37

Page 161

H e ba. For e > 0 choose nc so that \[in— fim\ £ for m, n 2^ nc. Then u(E)—n„(E) =

lim^^ (nm(E)—fi„{E)), from which it follows that Jjt« — | :£ e for n 5? ?ie. Hence //„ -

> ft, which proves that

H e ba. For e > 0 choose nc so that \[in— fim\ £ for m, n 2^ nc. Then u(E)—n„(E) =

lim^^ (nm(E)—fi„{E)), from which it follows that Jjt« — | :£ e for n 5? ?ie. Hence //„ -

> ft, which proves that

**ba**(**S**, E, X) is complete. It follows, therefore, that**ba**(**S**, 27, ...Page 311

The right hand side is independent of n, contradicting the supposition that there

was a set Gne Z with \f(n{Gn)\ > n f°r eacn integer n. Q.E.D. Next we turn to an

investigation of the space

The right hand side is independent of n, contradicting the supposition that there

was a set Gne Z with \f(n{Gn)\ > n f°r eacn integer n. Q.E.D. Next we turn to an

investigation of the space

**ba**(**S**, Z). 9 Theorem. The space**ba**(**S**, Z) is weakly ...Page 340

13 Show that the space bs is isometrically isomorphic with the space l^. Show

how this ... 17 Show that a sequence {An} of elements of

weakly to an element A €

13 Show that the space bs is isometrically isomorphic with the space l^. Show

how this ... 17 Show that a sequence {An} of elements of

**ba**(**S**, E) convergeweakly to an element A €

**ba**(**S**, E) if and only if there exists a non- negative n e ...### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

79 other sections not shown

### Other editions - View all

### Common terms and phrases

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact