Linear Operators: General theory |
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Page xvi
... elements , i.e. , A = B if and only if ACB and BC A. 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 BC A. 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 € A and b € 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 € A and b € 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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ