Linear Operators: General theory |
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Page 132
... singular , then 2 is also μ - singular . ' n 14 THEOREM . ( Lebesgue decomposition ) Let ( S , E , μ ) be a measure space . Then every finite countably additive measure 2 defined on Σ is uniquely representable as a sum λ = a + ß where x ...
... singular , then 2 is also μ - singular . ' n 14 THEOREM . ( Lebesgue decomposition ) Let ( S , E , μ ) be a measure space . Then every finite countably additive measure 2 defined on Σ is uniquely representable as a sum λ = a + ß where x ...
Page 565
... singular . Show that the set of all non - singular matrix solutions are precisely the matrices Y ( t ) C where C is any n × n constant , non- singular matrix . 26 Let A ( t ) have period p > 0 ; that is , A ( t + p ) = A ( t ) for all ...
... singular . Show that the set of all non - singular matrix solutions are precisely the matrices Y ( t ) C where C is any n × n constant , non- singular matrix . 26 Let A ( t ) have period p > 0 ; that is , A ( t + p ) = A ( t ) for all ...
Page 794
... singular non - self - adjoint differential operators of the second order . Doklady Akad . Nauk SSSR ( N. S. ) 85 , 41–44 ( 1952 ) . ( Russian ) Math . Rev. 14 , 473 ( 1953 ) . 10. Investigation of the spectrum and expansion in ...
... singular non - self - adjoint differential operators of the second order . Doklady Akad . Nauk SSSR ( N. S. ) 85 , 41–44 ( 1952 ) . ( Russian ) Math . Rev. 14 , 473 ( 1953 ) . 10. Investigation of the spectrum and expansion in ...
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