Linear Operators: General theory |
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Page 554
... bounded operator T : X。→ Yr has an extension ( with the same norm ) TX → Yr if and only if there is a projection ( of norm 1 ) from X onto X. Thus Kakutani [ 6 ] proved that X is a Hilbert space if and only if an arbitrary bounded ...
... bounded operator T : X。→ Yr has an extension ( with the same norm ) TX → Yr if and only if there is a projection ( of norm 1 ) from X onto X. Thus Kakutani [ 6 ] proved that X is a Hilbert space if and only if an arbitrary bounded ...
Page 600
... bounded operator , the spectrum may be a bounded set , an unbounded set , the void set , or even the whole plane . This is observed in Exercise 10.1 . We exclude the last possibility , and suppose throughout this section that o ( T ) is ...
... bounded operator , the spectrum may be a bounded set , an unbounded set , the void set , or even the whole plane . This is observed in Exercise 10.1 . We exclude the last possibility , and suppose throughout this section that o ( T ) is ...
Page 641
... bounded linear operator ) or the problem ex- pressed by the equations . a 22 ( 1 ' ) y ( s , t ) = Ət as2 y ( s , t ) ... operator A with non - void resolvent set . Specifically , to each function f analytic on σ ( 4 ) and at infinity we ...
... bounded linear operator ) or the problem ex- pressed by the equations . a 22 ( 1 ' ) y ( s , t ) = Ət as2 y ( s , t ) ... operator A with non - void resolvent set . Specifically , to each function f analytic on σ ( 4 ) and at infinity we ...
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