Linear Operators: General theory |
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Page 373
... fact that a linear manifold which is not dense in the entire space has a non - zero orthogonal complement ( proved in 4.4 ) was proved without the assumption of separability by F. Riesz [ 8 ] . His proof follows the lines of an argument ...
... fact that a linear manifold which is not dense in the entire space has a non - zero orthogonal complement ( proved in 4.4 ) was proved without the assumption of separability by F. Riesz [ 8 ] . His proof follows the lines of an argument ...
Page 608
... fact that a closed linear operator on an arbitrary complex B - space has non - void spectrum was proved by Taylor [ 12 ] . A special case of the fact that max o ( T ) = lim , T1 / n was proved by Beurling [ 1 ] , and the general case by ...
... fact that a closed linear operator on an arbitrary complex B - space has non - void spectrum was proved by Taylor [ 12 ] . A special case of the fact that max o ( T ) = lim , T1 / n was proved by Beurling [ 1 ] , and the general case by ...
Page 680
... fact which will be needed later . Now let g = ( I - T1 ) e M1 with f ( s ) ≤ K. Then A ( T1 , n ) ( g , s ) = n1 [ ƒ ( s ) —T ( f , s ) ] and thus V ( n , ... , n ) s ) nk ) ( g , 8 ) | ≤ 2K¦n1 for almost all s . This shows that , for ...
... fact which will be needed later . Now let g = ( I - T1 ) e M1 with f ( s ) ≤ K. Then A ( T1 , n ) ( g , s ) = n1 [ ƒ ( s ) —T ( f , s ) ] and thus V ( n , ... , n ) s ) nk ) ( g , 8 ) | ≤ 2K¦n1 for almost all s . This shows that , for ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ