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Page 249
Nelson Dunford, Jacob T. Schwartz. PROOF . The identity \ x + y2 + | xy | 2 = 2x2 + 2 | y | 2 , x , yes , called the parallelogram identity , follows immediately from the axioms . = If 8 inf x - k the preceding identity shows that kЄK k ...
Nelson Dunford, Jacob T. Schwartz. PROOF . The identity \ x + y2 + | xy | 2 = 2x2 + 2 | y | 2 , x , yes , called the parallelogram identity , follows immediately from the axioms . = If 8 inf x - k the preceding identity shows that kЄK k ...
Page 414
... identity , there is a neighborhood N of the identity such that N - NC M. Thus , any neighborhood of k 414 V.2.2 v . CONVEX SETS AND WEAK TOPOLOGIES.
... identity , there is a neighborhood N of the identity such that N - NC M. Thus , any neighborhood of k 414 V.2.2 v . CONVEX SETS AND WEAK TOPOLOGIES.
Page 479
... identity on X * . Thus ( T * ) - 1 exists , is in B ( X * , Y * ) , and equals ( T - 1 ) * . Conversely , if ( T ... identity 2 ( Tx , y ) = ( x , T VI.2.6 ADJOINTS 479.
... identity on X * . Thus ( T * ) - 1 exists , is in B ( X * , Y * ) , and equals ( T - 1 ) * . Conversely , if ( T ... identity 2 ( Tx , y ) = ( x , T VI.2.6 ADJOINTS 479.
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