Linear Operators: General theory |
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Page 62
... shown that the domain Yo of g is equal to X. For the purposes of an indirect proof , assuine the existence of a vector y , in X but not in 9o . Every vector in the manifold Y1 spanned by Yo and y1 has a unique representation in the form ...
... shown that the domain Yo of g is equal to X. For the purposes of an indirect proof , assuine the existence of a vector y , in X but not in 9o . Every vector in the manifold Y1 spanned by Yo and y1 has a unique representation in the form ...
Page 83
... shown by Banach [ 7 ] ( see also Banach [ 1 ; Chap . 1 ] and Kuratowski [ 1 ] ) . Conditions of this nature are extended to polynomial operators by Mazur and Orlicz [ 2 ] . It is sometimes useful to define a notion of " continuity " of ...
... shown by Banach [ 7 ] ( see also Banach [ 1 ; Chap . 1 ] and Kuratowski [ 1 ] ) . Conditions of this nature are extended to polynomial operators by Mazur and Orlicz [ 2 ] . It is sometimes useful to define a notion of " continuity " of ...
Page 553
... shown that in Hilbert space C is a maximal two - sided ideal . We have seen in Theorems 7.4 and 8.12 that in the spaces C and L1 , F C C C WCP . Grothendieck [ 4 ; p . 153 ] proved that in C , the ideals W and P coin- cide . This is not ...
... shown that in Hilbert space C is a maximal two - sided ideal . We have seen in Theorems 7.4 and 8.12 that in the spaces C and L1 , F C C C WCP . Grothendieck [ 4 ; p . 153 ] proved that in C , the ideals W and P coin- cide . This is not ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ