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 TX and U : Y - > Y 3 are linear transformations , and X , Y , Z are linear spaces ...
... 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 TX and U : Y - > Y 3 are linear transformations , and X , Y , Z are linear spaces ...
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 T. 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 T. The proof of Theorem 9 will be based on the following lemma . 10 LEMMA . If g ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ