Linear Operators: General theory |
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Page 169
... Show that there need not exist any containing A such that v ( u , E ) = 0 . - 3 Suppose that S is the interval ... Show that a real valued function ƒ is u - measurable if and only if it is continuous at every point not lying in a certain ...
... Show that there need not exist any containing A such that v ( u , E ) = 0 . - 3 Suppose that S is the interval ... Show that a real valued function ƒ is u - measurable if and only if it is continuous at every point not lying in a certain ...
Page 345
... Show that a subset of A ( D ) is weakly sequentially compact if and only if it is bounded and quasi - equicontinuous on the boundary of D. Show that A ( D ) is never weakly complete and never reflexive . Show that A ( D ) is a closed ...
... Show that a subset of A ( D ) is weakly sequentially compact if and only if it is bounded and quasi - equicontinuous on the boundary of D. Show that A ( D ) is never weakly complete and never reflexive . Show that A ( D ) is a closed ...
Page 360
... Show that for any f in CBV , ( S „ f ) ( x ) → f ( x ) uniformly in æ . 24 Suppose ( i ) , ( ii ) of the last exercise . Show that if ƒ is in BV then ( Sf ) ( x ) → f ( x ) at each point x where f is continuous . 25 Suppose that ( Sf ) ...
... Show that for any f in CBV , ( S „ f ) ( x ) → f ( x ) uniformly in æ . 24 Suppose ( i ) , ( ii ) of the last exercise . Show that if ƒ is in BV then ( Sf ) ( x ) → f ( x ) at each point x where f is continuous . 25 Suppose that ( Sf ) ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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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