Linear Operators: General theory |
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Page 249
Nelson Dunford, Jacob T. Schwartz. PROOF . The identity | x + y2 + | x — y | 2 = 2 | x | 2 + 2 | y | 2 , x , yes , called the parallelogram identity , follows immediately from the axioms . If 8 inf x - k the preceding identity shows that ...
Nelson Dunford, Jacob T. Schwartz. PROOF . The identity | x + y2 + | x — y | 2 = 2 | x | 2 + 2 | y | 2 , x , yes , called the parallelogram identity , follows immediately from the axioms . If 8 inf x - k the preceding identity shows that ...
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.2.6 479 ADJOINTS.
... 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.2.6 479 ADJOINTS.
Page 661
... identity = ( * ) Tn = A ( n ) - n - n n -1 A ( n − 1 ) shows that { T / n } is bounded and hence , by II.1.18 , the set of x for which Tx / n → 0 is a closed linear manifold . Thus X is a closed linear manifold and , since a ...
... identity = ( * ) Tn = A ( n ) - n - n n -1 A ( n − 1 ) shows that { T / n } is bounded and hence , by II.1.18 , the set of x for which Tx / n → 0 is a closed linear manifold . Thus X is a closed linear manifold and , since a ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ