## Linear Operators: General theory |

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Page 38

The term quotient space is sometimes used instead of factor space. The mapping

of 36 onto 36/2JJ, defined by x -> x is called the natural homomorphism of 36

onto X/9JJ. It is a linear transformation. Unless otherwise stated, the

field ...

The term quotient space is sometimes used instead of factor space. The mapping

of 36 onto 36/2JJ, defined by x -> x is called the natural homomorphism of 36

onto X/9JJ. It is a linear transformation. Unless otherwise stated, the

**coefficient**field ...

Page 229

The

where C is any closed rectifiable Jordan curve in the annulus a < \z— Zq\ < /S

which separates the circles |z— z0| = a and |z— z0| = /3 and which is traversed in

the ...

The

**coefficients**av are given by the formulas i r /(«) . a„ = — oa, P = 0, ±1, ±2,where C is any closed rectifiable Jordan curve in the annulus a < \z— Zq\ < /S

which separates the circles |z— z0| = a and |z— z0| = /3 and which is traversed in

the ...

Page 359

For / in Lv f„ = (2*)-^ J* f(x)e-^dx is called the nth Fourier

formal series — 00 is called the Fourier series of f. 18 Show that if {c„} is a

sequence with |c„|2 < oo, then there is some / in L2 whose nth Fourier

is c„.

For / in Lv f„ = (2*)-^ J* f(x)e-^dx is called the nth Fourier

**coefficient**of f and theformal series — 00 is called the Fourier series of f. 18 Show that if {c„} is a

sequence with |c„|2 < oo, then there is some / in L2 whose nth Fourier

**coefficient**is c„.

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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