## Linear Operators: General theory |

### From inside the book

Results 1-3 of 77

Page 204

Since ^(FJ = Js^/n^K^^) does not converge to

follows from the dominated convergence theorem (6.16) that there is a point sjjj in

Sai for which /„(*£ ) is defined for all n and for which the sequence {/„(«£)} does ...

Since ^(FJ = Js^/n^K^^) does not converge to

**zero**and since 0 :g fn(sai) 2a 1 itfollows from the dominated convergence theorem (6.16) that there is a point sjjj in

Sai for which /„(*£ ) is defined for all n and for which the sequence {/„(«£)} does ...

Page 452

If A is a subset of X, and p is in A, then there exists a non-

functional tangent to A at p if and only if the cone B with vertex p generated by A

is not dense in X. Proof. If q J K, then, by 2.12 we can find a functional / and a real

...

If A is a subset of X, and p is in A, then there exists a non-

**zero**continuous linearfunctional tangent to A at p if and only if the cone B with vertex p generated by A

is not dense in X. Proof. If q J K, then, by 2.12 we can find a functional / and a real

...

Page 557

polynomials S{, i = 2, . . ., k such that Si(T)xi = 0. If R = iSj • S2 - • -Sk, then R(T)xt =

0, and consequently R(T)x = 0 for all a;ej. Thus a non-

**zero**polynomial Sx such that S1(T)x1 = 0. In the same way, there exist non-**zero**polynomials S{, i = 2, . . ., k such that Si(T)xi = 0. If R = iSj • S2 - • -Sk, then R(T)xt =

0, and consequently R(T)x = 0 for all a;ej. Thus a non-

**zero**polynomial R exists ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

a-finite Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear functional convex set Corollary countably additive Definition denote dense Doklady Akad element equivalent everywhere exists finite dimensional follows from Theorem function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative non-zero normed linear space open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space valued function vector space weak topology weakly compact weakly sequentially compact zero