Linear Operators: General theory |
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Page 226
... integral theo- rem states that √ ( xx = 0 . The validity of this theorem ... integral theorem may be reworded in a somewhat more gener- al form . To state ... square mesh , and let U be the union of all open squares of the mesh whose ...
... integral theo- rem states that √ ( xx = 0 . The validity of this theorem ... integral theorem may be reworded in a somewhat more gener- al form . To state ... square mesh , and let U be the union of all open squares of the mesh whose ...
Page 519
... square is compact . 58 Let ( S , E , u ) be a positive finite measure space and K an essentially bounded measurable ... integrable functions on [ 0 , 1 ] . Represent the general linear operators in B ( L , L ) , B ( L , 4 ) , B ( 1 , L ) ...
... square is compact . 58 Let ( S , E , u ) be a positive finite measure space and K an essentially bounded measurable ... integrable functions on [ 0 , 1 ] . Represent the general linear operators in B ( L , L ) , B ( L , 4 ) , B ( 1 , L ) ...
Page 781
... integrable square of the system of differential equations . —y ' + P ( t ) y = λy . Doklady Akad . Nauk SSSR ( N. S. ) 95 , 217-220 ( 1954 ) . ( Russian ) Math . Rev. 15 , 957 ( 1954 ) . Lifšic , I. M. 1 . 2 . 3 . On the theory of ...
... integrable square of the system of differential equations . —y ' + P ( t ) y = λy . Doklady Akad . Nauk SSSR ( N. S. ) 95 , 217-220 ( 1954 ) . ( Russian ) Math . Rev. 15 , 957 ( 1954 ) . Lifšic , I. M. 1 . 2 . 3 . On the theory of ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ