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 x → a + x , where a eØ and a € X , are called scalar multiplication by x , and translation by a , respectively . A ...
... vector space are called vectors . The elements of the coefficient field are called scalars . The operations → ax and x → a + x , where a eØ and a € X , are called scalar multiplication by x , and translation by a , respectively . A ...
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 , and the set { x * μ \ x * € X * , | x * | ≤1 } _of_numerical measures is weakly sequentially compact as a subset of ca ( S , E ) . PROOF ... 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 , E ) . PROOF ... 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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian 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