Linear Operators: General theory |
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Page 838
space of, definition, IV.2.24 (242) properties, IV. 15 Annihilator of a set, II.4.17 (72
) Arzela theorem, on continuity of limit function, IV.6.11 (268) remarks concerning,
(383) Aseoli-Arzela theorem, on compactness of continuous functions, IV.6.7 ...
space of, definition, IV.2.24 (242) properties, IV. 15 Annihilator of a set, II.4.17 (72
) Arzela theorem, on continuity of limit function, IV.6.11 (268) remarks concerning,
(383) Aseoli-Arzela theorem, on compactness of continuous functions, IV.6.7 ...
Page 840
Closed orthonormal system, definition, IV.14.1 (357) study of, IV.14 Closed set,
definition, 1.4.3 (10) properties, 1.4.4-5 (10) Closed sphere, II.4.1 (70) Closed unit
sphere, II.3.1 (59) Closure of a set, criterion to be in, 1.7.2 (27) definition, 1.4.9 ...
Closed orthonormal system, definition, IV.14.1 (357) study of, IV.14 Closed set,
definition, 1.4.3 (10) properties, 1.4.4-5 (10) Closed sphere, II.4.1 (70) Closed unit
sphere, II.3.1 (59) Closure of a set, criterion to be in, 1.7.2 (27) definition, 1.4.9 ...
Page 844
5 Lebesgue, III.5.17-18 (142-143) Extensions of linear operators, VI.2.5 (478), (
554) Extremal point and subset, definitions V.8.1 (439) examples and properties,
V.ll.1-6 (457-458) remarks on, (400), (473) study of, V.8 Extremally disconnected,
...
5 Lebesgue, III.5.17-18 (142-143) Extensions of linear operators, VI.2.5 (478), (
554) Extremal point and subset, definitions V.8.1 (439) examples and properties,
V.ll.1-6 (457-458) remarks on, (400), (473) study of, V.8 Extremally disconnected,
...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries 84 | 34 |
Copyright | |
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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 convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma 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 properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero