Linear Operators: General theory |
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Page 781
... ( Russian ) Math . Rev. 11 , 720 ( 1950 ) . 4 . 5 . Proof of the theorem on the expansion in eigenfunctions of self - adjoint differential operators . Doklady Akad . Nauk SSSR ( N. S. ) 73 , 651-654 ( 1950 ) . ( Russian ) Math . Rev. 12 ...
... ( Russian ) Math . Rev. 11 , 720 ( 1950 ) . 4 . 5 . Proof of the theorem on the expansion in eigenfunctions of self - adjoint differential operators . Doklady Akad . Nauk SSSR ( N. S. ) 73 , 651-654 ( 1950 ) . ( Russian ) Math . Rev. 12 ...
Page 794
... ( Russian . English summary ) Math . Rev. 2 , 104 ( 1941 ) . 8. Spectral functions of a symmetric operator . Izvestiya Akad . Nauk SSSR ( N. S. ) 4 , 277-318 ( 1940 ) . ( Russian . English summary ) Math . Rev. 2 , 105 ( 1941 ) . 9. On ...
... ( Russian . English summary ) Math . Rev. 2 , 104 ( 1941 ) . 8. Spectral functions of a symmetric operator . Izvestiya Akad . Nauk SSSR ( N. S. ) 4 , 277-318 ( 1940 ) . ( Russian . English summary ) Math . Rev. 2 , 105 ( 1941 ) . 9. On ...
Page 811
... ( Russian ) Math . Rev. 14 , 882 ( 1953 ) . 16. Operators with degenerate characteristic functions . Doklady Akad . Nauk SSSR ( N. S. ) 93 , 985-988 ( 1953 ) . ( Russian ) Math . Rev. 15 , 803 ( 1954 ) . 17. Completely continuous ...
... ( Russian ) Math . Rev. 14 , 882 ( 1953 ) . 16. Operators with degenerate characteristic functions . Doklady Akad . Nauk SSSR ( N. S. ) 93 , 985-988 ( 1953 ) . ( Russian ) Math . Rev. 15 , 803 ( 1954 ) . 17. Completely continuous ...
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