Linear Operators: General theory |
From inside the book
Results 1-3 of 88
Page 145
... space X. It will be shown in this section that if ( S , Σ , μ ) is a measure space the various linear vector spaces of measurable and integrable functions we have encountered are complete metric spaces . Criteria for u - measurability ...
... space X. It will be shown in this section that if ( S , Σ , μ ) is a measure space the various linear vector spaces of measurable and integrable functions we have encountered are complete metric spaces . Criteria for u - measurability ...
Page 347
... measure or a null set . 50 Show that no space equivalent to a space C ( S ) is equivalent to a closed subspace of a space ba ( S , Σ ) unless both are finite dimen- sional . 51 Show that no space L „ ( S , Σ , μ ) , 1 < p < ∞ , is ...
... measure or a null set . 50 Show that no space equivalent to a space C ( S ) is equivalent to a closed subspace of a space ba ( S , Σ ) unless both are finite dimen- sional . 51 Show that no space L „ ( S , Σ , μ ) , 1 < p < ∞ , is ...
Page 405
... space s is , of course , the space of all real sequences x = [ x ] as distinct from l2 , which is the subspace of s determined by the condition < ∞ . The measure His countably additive ; the subset ↳ of s is of μ - measure zero ; the ...
... space s is , of course , the space of all real sequences x = [ x ] as distinct from l2 , which is the subspace of s determined by the condition < ∞ . The measure His countably additive ; the subset ↳ of s is of μ - measure zero ; the ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
49 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ