Linear Operators: General theory |
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Page 2
... elements , i.e. , A = B if and only if ACB and BCA . The set A is said to be a proper subset of the set B if ACB and A B. The notation AC B , or BƆ A , will mean that A is a proper subset of B. The complement of a set A relative to a ...
... elements , i.e. , A = B if and only if ACB and BCA . The set A is said to be a proper subset of the set B if ACB and A B. The notation AC B , or BƆ A , will mean that A is a proper subset of B. The complement of a set A relative to a ...
Page 34
... elements of G , the symbol A - 1is written for the set of elements of the form a - 1 where a € A , AB de- notes the set of elements of the form ab with a e A and be B , gA de- notes the set of elements ga with a e A , and gAh denotes ...
... elements of G , the symbol A - 1is written for the set of elements of the form a - 1 where a € A , AB de- notes the set of elements of the form ab with a e A and be B , gA de- notes the set of elements ga with a e A , and gAh denotes ...
Page 36
... elements form a group under multipli- cation . The unit of this group in a field will be written as 1 instead of e ... elements of a vector space are called vectors . The elements of the coefficient field are called scalars . The ...
... elements form a group under multipli- cation . The unit of this group in a field will be written as 1 instead of e ... elements of a vector space are called vectors . The elements of the coefficient field are called scalars . The ...
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 converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ