Linear Operators: General theory |
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Page 88
... condition is sufficient . Bonsall [ 1 ] showed that the separa- bility condition cannot be dropped . Ingleton [ 1 ] has given conditions ... boundary value problems . We refer the reader to the papers of Garabedian [ 1 ] , Garabedian and ...
... condition is sufficient . Bonsall [ 1 ] showed that the separa- bility condition cannot be dropped . Ingleton [ 1 ] has given conditions ... boundary value problems . We refer the reader to the papers of Garabedian [ 1 ] , Garabedian and ...
Page 743
... boundary conditions . Trans . Amer . Math . Soc . 45 , 369-442 ( 1939 ) . Two sided ideals and congruences in the ring of bounded operators in Hilbert space . Ann . of Math . ( 2 ) 42 , 839-873 ( 1941 ) . 3. Symmetric transformations in ...
... boundary conditions . Trans . Amer . Math . Soc . 45 , 369-442 ( 1939 ) . Two sided ideals and congruences in the ring of bounded operators in Hilbert space . Ann . of Math . ( 2 ) 42 , 839-873 ( 1941 ) . 3. Symmetric transformations in ...
Page 818
... boundary conditions . Doklady Akad . Nauk SSSR ( N. S. ) 65 , 433–436 ( 1949 ) . ( Russian ) Math . Rev. 11 , 38-39 ( 1950 ) . 3 . 2. On linear boundary problems for differential equations . Doklady Akad . Nauk SSSR ( N. S. ) 65 , 785 ...
... boundary conditions . Doklady Akad . Nauk SSSR ( N. S. ) 65 , 433–436 ( 1949 ) . ( Russian ) Math . Rev. 11 , 38-39 ( 1950 ) . 3 . 2. On linear boundary problems for differential equations . Doklady Akad . Nauk SSSR ( N. S. ) 65 , 785 ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ