Linear Operators: General theory |
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Page xvi
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B ... means that the following distributive laws hold : aεA x x a = U ( xa ) , xu ( na ) aed a € A ad = = n ( cua ) . açd ...
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B ... means that the following distributive laws hold : aεA x x a = U ( xa ) , xu ( na ) aed a € A ad = = n ( cua ) . açd ...
Page 2
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B ... means that the following distributive laws hold : aε A x a = aed U ( xa ) , xU ( a ) = a € A ad Ụ a € A bu ... Uc ...
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B ... means that the following distributive laws hold : aε A x a = aed U ( xa ) , xU ( a ) = a € A ad Ụ a € A bu ... Uc ...
Page 660
... mean and pointwise convergence theorems for the contin- uous case . Section 8 is concerned with a certain class of operators T for which the sequence of averages ( N - 1 - T } converges in the uniform topology of operators . Finally ...
... mean and pointwise convergence theorems for the contin- uous case . Section 8 is concerned with a certain class of operators T for which the sequence of averages ( N - 1 - T } converges in the uniform topology of operators . Finally ...
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