Linear Operators: General theory |
From inside the book
Results 1-3 of 89
Page 17
... compact if its closure is compact in its relative topology . It should be noted that a subset ACX is compact in its relative topology if and only if every covering of A by open sets in X contains a finite subcovering . A well - known ...
... compact if its closure is compact in its relative topology . It should be noted that a subset ACX is compact in its relative topology if and only if every covering of A by open sets in X contains a finite subcovering . A well - known ...
Page 483
... compact , then TS is compact in the Y * topology of Y and thus x ( TS ) is compact and hence closed in the Y * topology of Y ** . Thus if T is weakly compact , ( i ) yields T ** ( S1 ) ≤ × ( TS ) . According to Theorem V.4.5 , S1 S ...
... compact , then TS is compact in the Y * topology of Y and thus x ( TS ) is compact and hence closed in the Y * topology of Y ** . Thus if T is weakly compact , ( i ) yields T ** ( S1 ) ≤ × ( TS ) . According to Theorem V.4.5 , S1 S ...
Page 485
... compact if and only if its adjoint is weakly compact . PROOF . Let T be weakly compact . Since the closed unit 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 ...
... compact if and only if its adjoint is weakly compact . PROOF . Let T be weakly compact . Since the closed unit 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 ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
40 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ