Linear Operators: General theory |
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Page 17
... continuous on the closed set A in the normal space X , the bounded function arctan f ( x ) has a continuous extension a ( x ) defined on X. The closed sets A and B = { x || x ( x ) | = π / 2 } are disjoint , and hence there is a continuous ...
... continuous on the closed set A in the normal space X , the bounded function arctan f ( x ) has a continuous extension a ( x ) defined on X. The closed sets A and B = { x || x ( x ) | = π / 2 } are disjoint , and hence there is a continuous ...
Page 381
... functional [ II . p . 593 ] . There are also a number of recent papers related to this result . For example , Halmos [ 5 ; Chap . 10 ] , Hewitt [ 3 ] and Edwards [ 1 ] consider functionals on the space of continuous functions on a ...
... functional [ II . p . 593 ] . There are also a number of recent papers related to this result . For example , Halmos [ 5 ; Chap . 10 ] , Hewitt [ 3 ] and Edwards [ 1 ] consider functionals on the space of continuous functions on a ...
Page 632
... continuous function defined for t > with values in X and suppose that f ( t ) dt < ∞o . If g ( t ) = S1T ( t — s ) f ( s ) ds , then g ( t ) is in D ( P ) , t Pg ( t ) = [ ' * PT ( t — s ) f ( s ) ds , and g and Pg are continuous functions ...
... continuous function defined for t > with values in X and suppose that f ( t ) dt < ∞o . If g ( t ) = S1T ( t — s ) f ( s ) ds , then g ( t ) is in D ( P ) , t Pg ( t ) = [ ' * PT ( t — s ) f ( s ) ds , and g and Pg are continuous functions ...
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