## Linear Operators: General theory |

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Page 10

If r, rt are two topologies in X, r is said to be stronger, or larger, than tx and Tj is

said to be weaker, or smaller, than t if r 2 rv The sets in t are called the

of (X, t). A neighborhood of the point p is an

neighborhood ...

If r, rt are two topologies in X, r is said to be stronger, or larger, than tx and Tj is

said to be weaker, or smaller, than t if r 2 rv The sets in t are called the

**open sets**of (X, t). A neighborhood of the point p is an

**open set**containing p. Aneighborhood ...

Page 84

some right-invariant (possibly non-definite) metric, then a homomorphism h : X ->

Y is an interior map into Y and has a closed kernel, A-1(0), if and only if the graph

of h is closed, and h maps each non-void

some right-invariant (possibly non-definite) metric, then a homomorphism h : X ->

Y is an interior map into Y and has a closed kernel, A-1(0), if and only if the graph

of h is closed, and h maps each non-void

**open set**onto a set whose closure ...Page 213

Let k be a finite positive measure defined an the Borel subsets of the closure of a

bounded

in a set AQG A(C) lim inf < r, MQ-*0 where C is a closed cube containing p, then ...

Let k be a finite positive measure defined an the Borel subsets of the closure of a

bounded

**open set**G of real Euclidean n-space En. Let 0 < r < oo. (a) // for each pin a set AQG A(C) lim inf < r, MQ-*0 where C is a closed cube containing p, then ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

79 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-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function 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 Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero