Linear Operators: General theory |
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Page 181
... preceding argument . Thus only formula [ * ] remains to be verified . By the argument used in the proof of Corollary 5 it is seen that it will be sufficient to prove [ * ] in the case when g is a positive real function . It is also ...
... preceding argument . Thus only formula [ * ] remains to be verified . By the argument used in the proof of Corollary 5 it is seen that it will be sufficient to prove [ * ] in the case when g is a positive real function . It is also ...
Page 266
... preceding theorem and the dominated convergence theorem of Lebesgue ( III.6.16 ) . Q.E.D. 5 THEOREM . Let S be an arbitrary topological space and K a bounded subset of C ( S ) . Then K is conditionally compact if and only if for every ε ...
... preceding theorem and the dominated convergence theorem of Lebesgue ( III.6.16 ) . Q.E.D. 5 THEOREM . Let S be an arbitrary topological space and K a bounded subset of C ( S ) . Then K is conditionally compact if and only if for every ε ...
Page 537
... preceding Exercise IV.14.34 . Show that if Tnf f in the norm of C for every ← fe C , then Taff in the norm of L , for every fe L 47 Let { 2 } be a real factor sequence which is of type ( C , C ) in the sense of the definition preceding ...
... preceding Exercise IV.14.34 . Show that if Tnf f in the norm of C for every ← fe C , then Taff in the norm of L , for every fe L 47 Let { 2 } be a real factor sequence which is of type ( C , C ) in the sense of the definition preceding ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ