Linear Operators: General theory |
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Page 90
... Invariant metrics in groups . A metric o on a ( multiplicative ) group G is said to be left - invariant if o ( gx , gy ) = g ( x , y ) for all g in G. It is said to be invariant if o ( gx , gy ) o ( x , y ) = g ( xg , yg ) for all g in ...
... Invariant metrics in groups . A metric o on a ( multiplicative ) group G is said to be left - invariant if o ( gx , gy ) = g ( x , y ) for all g in G. It is said to be invariant if o ( gx , gy ) o ( x , y ) = g ( xg , yg ) for all g in ...
Page 91
... invariant metric and is complete under each invariant metric . Thus every complete linear metric space can be metrized to be an F - space . Further , a normed linear space is a B - space provided it is complete under some equivalent ...
... invariant metric and is complete under each invariant metric . Thus every complete linear metric space can be metrized to be an F - space . Further , a normed linear space is a B - space provided it is complete under some equivalent ...
Page 516
... invariant . 39 Let S be a compact Hausdorff space and a continuous function on S to S. Show that there is a regular countably additive non - negative measure μ defined for all Borel sets in S with the prop- erties that μ is not ...
... invariant . 39 Let S be a compact Hausdorff space and a continuous function on S to S. Show that there is a regular countably additive non - negative measure μ defined for all Borel sets in S with the prop- erties that μ is not ...
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