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 x , 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 x , 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 } = 4. 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 } = 4. We ...
Page 318
... Vector Valued Measures The theorems on spaces of set functions proved in the last section permit us to develop a more satisfactory theory of vector valued count- ably additive set functions ( briefly , vector valued measures ) than we ...
... Vector Valued Measures The theorems on spaces of set functions proved in the last section permit us to develop a more satisfactory theory of vector valued count- ably additive set functions ( briefly , vector valued measures ) than we ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ