Linear Operators: General theory |
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Page 539
... Schmidt [ 1 ] , to whom the geometrical terminology in linear space theory is due . Compact and weakly compact operators . The concept of a compact ( or completely continuous ) operator is essentially due to Hilbert ... operator to map weakly ...
... Schmidt [ 1 ] , to whom the geometrical terminology in linear space theory is due . Compact and weakly compact operators . The concept of a compact ( or completely continuous ) operator is essentially due to Hilbert ... operator to map weakly ...
Page 609
... Schmidt [ 2 ] depending on the possibility ( in Hilbert space ) of approximating the compact operator by operators with finite dimensional ranges . Probably the most ingenious and elementary approach is due to F. Riesz [ 4 ] and is ...
... Schmidt [ 2 ] depending on the possibility ( in Hilbert space ) of approximating the compact operator by operators with finite dimensional ranges . Probably the most ingenious and elementary approach is due to F. Riesz [ 4 ] and is ...
Contents
Preliminary Concepts | 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 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