Linear Operators: General theory |
From inside the book
Results 1-3 of 64
Page 485
... sphere S * of Y * is Y - compact ( V.4.2 ) , it follows from Lemma 7 and Lemma I.5.7 that T * S * is compact in the X ** topology of X * . Hence T * is weakly compact . Conversely , if T * is weakly compact , it follows from Lemma 7 ...
... sphere S * of Y * is Y - compact ( V.4.2 ) , it follows from Lemma 7 and Lemma I.5.7 that T * S * is compact in the X ** topology of X * . Hence T * is weakly compact . Conversely , if T * is weakly compact , it follows from Lemma 7 ...
Page 512
... sphere of B ( X , Y ) is compact in the weak operator topology , Y is reflexive . 7 Define the BWO topology for B ... sphere S of B ( X , Y ) . Show by the method of proof of V.5.4 that if Y is reflexive then a fundamental set of ...
... sphere of B ( X , Y ) is compact in the weak operator topology , Y is reflexive . 7 Define the BWO topology for B ... sphere S of B ( X , Y ) . Show by the method of proof of V.5.4 that if Y is reflexive then a fundamental set of ...
Page 718
... sphere is ≤K . Putting h * ( x ) = supo < r < 1 | h ( rx ) | for | x | = 1 , show that there exists an absolute constant Cn , v such that the integral of h ** over the surface of the unit sphere is at most C ,,, K . Show that lim , h ...
... sphere is ≤K . Putting h * ( x ) = supo < r < 1 | h ( rx ) | for | x | = 1 , show that there exists an absolute constant Cn , v such that the integral of h ** over the surface of the unit sphere is at most C ,,, K . Show that lim , h ...
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