Linear Operators: General theory |
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Page 73
... s = [ $ 1 , $ 2 , ... ] . Show that if the norm of s be defined as = lub s , 1 < i < ∞ m is a B - space . 22 ... LIM Sn ( a ) LIM s1 = LIM $ n + 1 ; ∞48 Sn ∞48 ∞48 = * ( s ) , show that ( b ) LIM ( as , + ẞtn ) = a LIM s2 + ẞ ...
... s = [ $ 1 , $ 2 , ... ] . Show that if the norm of s be defined as = lub s , 1 < i < ∞ m is a B - space . 22 ... LIM Sn ( a ) LIM s1 = LIM $ n + 1 ; ∞48 Sn ∞48 ∞48 = * ( s ) , show that ( b ) LIM ( as , + ẞtn ) = a LIM s2 + ẞ ...
Page 219
Nelson Dunford, Jacob T. Schwartz. • sin2n ( t - s ) lim N∞∞ and ∞ n ( t - s ) f ( s ) ds = f ( t ) = f ( t ) , lim ne - n ( t - s ) f ( s ) ds 348 t each holding in the Lebesgue set of f . Instead of proving Theorem 10 directly we ...
Nelson Dunford, Jacob T. Schwartz. • sin2n ( t - s ) lim N∞∞ and ∞ n ( t - s ) f ( s ) ds = f ( t ) = f ( t ) , lim ne - n ( t - s ) f ( s ) ds 348 t each holding in the Lebesgue set of f . Instead of proving Theorem 10 directly we ...
Page 339
... lim , § ( " ) , i = 1 , 2 , . . . all exist , and that such a sequence con- verges weakly to the element x { } . Show that if p condition describes co - convergence in ↳ Si = c * . = 1 , the same 5 Show that no space B ( S ... ( S ) is weakly ...
... lim , § ( " ) , i = 1 , 2 , . . . all exist , and that such a sequence con- verges weakly to the element x { } . Show that if p condition describes co - convergence in ↳ Si = c * . = 1 , the same 5 Show that no space B ( S ... ( S ) is weakly ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ