## Linear Operators: General theory |

### From inside the book

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Page 3

The characteristic function Xe of a set jE is the real function defined by the

equations Xe(s) — If s * E, and %£(s) = 0, s 4 E. ... By the extended

system we mean the

the ...

The characteristic function Xe of a set jE is the real function defined by the

equations Xe(s) — If s * E, and %£(s) = 0, s 4 E. ... By the extended

**real number**system we mean the

**real numbers**with the symbols +oo and — oo adjoined; bythe ...

Page 4

If </> is the %roid subset of the

sup <f>, + oo = inf <f>. If A is an infinite set of

sup A denotes the infimum of all numbers b with the property that only a finite set

of ...

If </> is the %roid subset of the

**real numbers**, it is conventional to take — oo =sup <f>, + oo = inf <f>. If A is an infinite set of

**real numbers**, then the symbol limsup A denotes the infimum of all numbers b with the property that only a finite set

of ...

Page 11

A subbase for this topology is given by all infinite intervals {-co, a), (b, +oo),

where a and b are either real or rational. The topology of the extended

A subbase for this topology is given by all infinite intervals {-co, a), (b, +oo),

where a and b are either real or rational. The topology of the extended

**real****numbers**has as a base the sets [-co, a), (a,b), (b, +oo], where a and b are**real****numbers**.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### 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