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Page 36
... vector space are called vectors . The elements of the coefficient field are called scalars . The operations a → xx and x → ax , where a eØ and a e X , are called scalar multiplication by a , and translation by a , respectively . A sum ...
... vector space are called vectors . The elements of the coefficient field are called scalars . The operations a → xx and x → ax , where a eØ and a e X , are called scalar multiplication by a , and translation by a , respectively . A sum ...
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 795
... vector lattices , I , II . 5 . 6 . 7 . I. J. Sci . Hirosima Univ . Ser . A. 12 , 17-35 ( 1942 ) . II . ibid . 12 , 217-234 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 545 ( 1949 ) . Some general theorems and convergence theorems in vector ...
... vector lattices , I , II . 5 . 6 . 7 . I. J. Sci . Hirosima Univ . Ser . A. 12 , 17-35 ( 1942 ) . II . ibid . 12 , 217-234 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 545 ( 1949 ) . Some general theorems and convergence theorems in vector ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ