Linear Operators: General theory |
From inside the book
Results 1-3 of 85
Page 103
... denote the class of functions equivalent to f ( i.e. all g such that f - g is a u - null function ) , and let F ( S , E , u , X ) denote the set of all such sets . [ f ] . If the following equations are used to define their left hand ...
... denote the class of functions equivalent to f ( i.e. all g such that f - g is a u - null function ) , and let F ( S , E , u , X ) denote the set of all such sets . [ f ] . If the following equations are used to define their left hand ...
Page 142
... denote a set in Σ , the symbol M with or without subscripts will denote a set in for which v ( u , M ) = 0 , and N with or without subscripts will denote a subset of a set M. To see that the complement of a set EUN in * is also in ...
... denote a set in Σ , the symbol M with or without subscripts will denote a set in for which v ( u , M ) = 0 , and N with or without subscripts will denote a subset of a set M. To see that the complement of a set EUN in * is also in ...
Page 469
... denote the unit sphere in the space of variables 1 , Xi - 1 Xi + 1 , ... , xn . Let at denote the positive square root { 1- ( a + ... + æ ; _ ? + æ ; + 22 + . . . + a ) } 1/2 , and a denote the corresponding negative + x - 1 square root ...
... denote the unit sphere in the space of variables 1 , Xi - 1 Xi + 1 , ... , xn . Let at denote the positive square root { 1- ( a + ... + æ ; _ ? + æ ; + 22 + . . . + a ) } 1/2 , and a denote the corresponding negative + x - 1 square root ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ