## Linear Operators: General theory |

### From inside the book

Results 1-3 of 74

Page 121

In the sequel the symbol / rather than [/] will be used for an element in Lv. We

observe that the

be regarded as applying to the spaces Lv. This observation is obvious in the case

of ...

In the sequel the symbol / rather than [/] will be used for an element in Lv. We

observe that the

**inequality**of Minkowski and (in ... the**inequality**of Holder maybe regarded as applying to the spaces Lv. This observation is obvious in the case

of ...

Page 248

The above

follows from the postulates for § that the Schwarz

is zero. Hence suppose that x ^ 0 y. For an arbitrary complex number a 0 g (x+a.y,

...

The above

**inequality**, known as the Schwarz**inequality**, will be proved first. Itfollows from the postulates for § that the Schwarz

**inequality**is valid if either x or yis zero. Hence suppose that x ^ 0 y. For an arbitrary complex number a 0 g (x+a.y,

...

Page 370

Nelson Dunford, Jacob T. Schwartz. and the equality is attained only by scalar

multiples of the Tchebicheff polynomial r„. 79 The

1S<£1 holds for each x in P„. 80 If n is odd, the

holds ...

Nelson Dunford, Jacob T. Schwartz. and the equality is attained only by scalar

multiples of the Tchebicheff polynomial r„. 79 The

**inequality**|«'(1)| ^ n2max \x{t)\ -1S<£1 holds for each x in P„. 80 If n is odd, the

**inequality**\x'(0)\ S n max \x(t)\holds ...

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### 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