## Linear Operators: General theory |

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Page 14

Q.E.D. 17 Lemma. // X, Y, Z are topological spaces, and if f : X Y and g : Y -> Z arc

used for a real or complex number; a scalar

Q.E.D. 17 Lemma. // X, Y, Z are topological spaces, and if f : X Y and g : Y -> Z arc

**continuous**, then the composite**function**fg is**continuous**. The term scalar will beused for a real or complex number; a scalar

**function**is a real or complex valued ...Page 381

10], Hewitt [3] and Edwards [1] consider functionals on the space of

sets. Arens [3] discussed certain sub-algebras of

10], Hewitt [3] and Edwards [1] consider functionals on the space of

**continuous****functions**on a locally compact Hausdorff space which vanish outside of compactsets. Arens [3] discussed certain sub-algebras of

**continuous functions**on a ...Page 841

criteria for the limit to be continuous, 1.7.7 (29), IV.6.11 (268) definition, 1.4.15 (13

) density in TM and L„, III.9.14 (170), IV.8.19 (298) existence of non-differentiable

criteria for the limit to be continuous, 1.7.7 (29), IV.6.11 (268) definition, 1.4.15 (13

) density in TM and L„, III.9.14 (170), IV.8.19 (298) existence of non-differentiable

**continuous functions**, 1.9.6 (33) existence on a normal space, 1.5.2 (15) ...### 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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a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional linear map linear operator linear topological space LP(S measurable functions 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 Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact