Linear Operators: General theory |
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Page 36
... linear combination of the vectors x , y , z . A linear subspace , subspace or linear manifold in a vector space , is a subset which contains all linear combinations of its vectors . The subspace spanned by , or determined by a given set ...
... linear combination of the vectors x , y , z . A linear subspace , subspace or linear manifold in a vector space , is a subset which contains all linear combinations of its vectors . The subspace spanned by , or determined by a given set ...
Page 37
... linear transformation on a linear space X is a homomorphism on the additive group X which commutes with the operations of multiplication by scalars . If T : X → Y and U : Y → 3 are linear transformations , and X , Y , Z are linear ...
... linear transformation on a linear space X is a homomorphism on the additive group X which commutes with the operations of multiplication by scalars . If T : X → Y and U : Y → 3 are linear transformations , and X , Y , Z are linear ...
Page 421
... linear space , and let I be a total subspace of X. Then the linear functionals on X which are continuous in the I topology are precisely the functionals in I. The proof of Theorem 9 will be based on the following lemma . 10 LEMMA . If g ...
... linear space , and let I be a total subspace of X. Then the linear functionals on X which are continuous in the I topology are precisely the functionals in I. The proof of Theorem 9 will be based on the following lemma . 10 LEMMA . If g ...
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 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ