Linear Operators: General theory |
From inside the book
Results 1-3 of 83
Page 373
... proved for closed linear manifolds in L , [ 0 , 1 ] by E. Fischer [ 2 ] . The 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 ...
... proved for closed linear manifolds in L , [ 0 , 1 ] by E. Fischer [ 2 ] . The 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 ...
Page 385
... proved independently by Cech [ 1 ] only slightly later . ( See also Stone [ 5 ] for an elementary treatment . ) Lemma 6.25 was proved in Stone [ 1 ; p . 465 ] -extensions of this re- sult are also found in Hewitt [ 5 ] and Kaplansky ...
... proved independently by Cech [ 1 ] only slightly later . ( See also Stone [ 5 ] for an elementary treatment . ) Lemma 6.25 was proved in Stone [ 1 ; p . 465 ] -extensions of this re- sult are also found in Hewitt [ 5 ] and Kaplansky ...
Page 463
... proved that in the case of a separable space these notions coincide with that of closure in the topology of X * . Alaoglu [ 1 ; p . 256 ] and Kakutani [ 2 ; p . 170 ] independently established the equivalence of these types of closure ...
... proved that in the case of a separable space these notions coincide with that of closure in the topology of X * . Alaoglu [ 1 ; p . 256 ] and Kakutani [ 2 ; p . 170 ] independently established the equivalence of these types of closure ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ