Linear Operators: General theory |
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Page 37
... linear transformation on a linear space X is a homomorphism on the additive group & which commutes with the operations of multiplication by scalars . If TX and U : Y Y 3 are linear transformations , and X , Y , Z are linear spaces over ...
... linear transformation on a linear space X is a homomorphism on the additive group & which commutes with the operations of multiplication by scalars . If TX and U : Y Y 3 are linear transformations , and X , Y , Z are linear spaces over ...
Page 418
... linear topological space X , and if K1 is compact , then some non - zero continuous linear functional on X separates K1 and K. 12 COROLLARY . If K is a closed convex subset of a locally convex linear topological space , and p & K , then ...
... linear topological space X , and if K1 is compact , then some non - zero continuous linear functional on X separates K1 and K. 12 COROLLARY . If K is a closed convex subset of a locally convex linear topological space , and p & K , then ...
Page 421
... linear space , and let г be a total subspace of X. Then the linear functionals on X which are continuous in the I topology are precisely the functionals in T. The proof of Theorem 9 will be based on the following lemma . 10 LEMMA . If g ...
... linear space , and let г be a total subspace of X. Then the linear functionals on X which are continuous in the I topology are precisely the functionals in T. The proof of Theorem 9 will be based on the following lemma . 10 LEMMA . If g ...
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