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 → ax and xax , where x € Ø and a € X , are called scalar multiplication by x , and translation by a , respectively . A sum ar + ...
... vector space are called vectors . The elements of the coefficient field are called scalars . The operations → ax and xax , where x € Ø and a € X , are called scalar multiplication by x , and translation by a , respectively . A sum ar + ...
Page 250
... vector in 4 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 } = H → A. We ...
... vector in 4 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 } = H → A. We ...
Page 319
... vector measure is bounded , is bounded , and the set { x * μ \ x * € X * , \ x * | ≤ 1 } of numerical measures is weakly sequentially compact as a subset of ca ( S , E ) ... vector IV.10.2 319 VECTOR VALUED MEASURES Vector Valued Measures.
... vector measure is bounded , is bounded , and the set { x * μ \ x * € X * , \ x * | ≤ 1 } of numerical measures is weakly sequentially compact as a subset of ca ( S , E ) ... vector IV.10.2 319 VECTOR VALUED MEASURES Vector Valued Measures.
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ