Linear Operators: General theory |
From inside the book
Results 1-3 of 59
Page 106
... simple functions . If for every E in with v ( u , E ) < ∞ , the product Zef of f with the characteristic function ... functions are M ( S , 2 , μ , X ) , M ( S , E , μ ) , M ( S ) and symbols besides TM ( S ) for the set of totally ...
... simple functions . If for every E in with v ( u , E ) < ∞ , the product Zef of f with the characteristic function ... functions are M ( S , 2 , μ , X ) , M ( S , E , μ ) , M ( S ) and symbols besides TM ( S ) for the set of totally ...
Page 108
... simple function " and " u - integrable simple function " will be used interchan- geably . For an EeΣ the integral over E of a μ - integrable simple func- tion h is defined by the equation n Σαμ ( ΕΕ ; ) . [ _h ( s ) u ( ds ) = √ f ( s ) ...
... simple function " and " u - integrable simple function " will be used interchan- geably . For an EeΣ the integral over E of a μ - integrable simple func- tion h is defined by the equation n Σαμ ( ΕΕ ; ) . [ _h ( s ) u ( ds ) = √ f ( s ) ...
Page 322
... function ƒ defined on S is u - simple if it is a finite linear combination of characteristic functions of sets in * ; this is evidently the case if and only if f is 2 - simple . It follows from Corollaries III.6.13 and III.6.14 that ƒ ...
... function ƒ defined on S is u - simple if it is a finite linear combination of characteristic functions of sets in * ; this is evidently the case if and only if f is 2 - simple . It follows from Corollaries III.6.13 and III.6.14 that ƒ ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ