Linear Operators: General theory |
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Page 36
... vector space are called vectors . The elements of the coefficient field are called scalars . The operations → ∞x and x → a + x , where a € Ø and a € X , are called scalar multiplication by a , and translation by a , respectively . A ...
... vector space are called vectors . The elements of the coefficient field are called scalars . The operations → ∞x and x → a + x , where a € Ø and a € X , are called scalar multiplication by a , and translation by a , respectively . A ...
Page 250
... vector in A has norm one and if every pair of distinct vectors in A are orthogonal . An orthonormal set is said to be complete if no non - zero vector is orthogonal to every vector in the set , i.e. , A is complete if { 0 } = A. We ...
... vector in A has norm one and if every pair of distinct vectors in A are orthogonal . An orthonormal set is said to be complete if no non - zero vector is orthogonal to every vector in the set , i.e. , A is complete if { 0 } = A. We ...
Page 319
... vector measure is bounded , and the set { x * μ \ x * € X * , x * | ≤ 1 } of numerical measures is weakly sequentially compact as a subset of ca ( S , Σ ) . PROOF . Since ... vector IV.10.2 319 VECTOR VALUED MEASURES Vector Valued Measures.
... vector measure is bounded , and the set { x * μ \ x * € X * , x * | ≤ 1 } of numerical measures is weakly sequentially compact as a subset of ca ( S , Σ ) . PROOF . Since ... vector IV.10.2 319 VECTOR VALUED MEASURES Vector Valued Measures.
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ