Linear Operators: General theory |
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Page 2
... elements , i.e. , A = B if and only if AC B and B C A. The set A is said to be a proper subset of the set B if ACB and AB . 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 AC B and B C A. The set A is said to be a proper subset of the set B if ACB and AB . 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 e 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 e 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 45
... element a ;, by 1 and all the other elements of the ith row and jth column by 0 and calculating the resulting determinant . Denoting the cofactor of a by A , it may be seen that [ * ] 22 det ( a ;; ) = Σ a¿¡ Aij n Σ ajj Ajj = Σ ajj Ajj ...
... element a ;, by 1 and all the other elements of the ith row and jth column by 0 and calculating the resulting determinant . Denoting the cofactor of a by A , it may be seen that [ * ] 22 det ( a ;; ) = Σ a¿¡ Aij n Σ ajj Ajj = Σ ajj Ajj ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ