Linear Operators: General theory |
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Page 581
... spectrum of an operator . = 7 Let T be the map in l „ , 1 ≤ p ≤∞ , defined by T [ §1 , §2 , . . . ] [ 2 , 3 ... spectrum σ ( E ) ? Find ƒ ( E ) for je F ( E ) . 9 For any bounded linear operator T show that 10 0 , ( T ) ≤ 0 , ( T ...
... spectrum of an operator . = 7 Let T be the map in l „ , 1 ≤ p ≤∞ , defined by T [ §1 , §2 , . . . ] [ 2 , 3 ... spectrum σ ( E ) ? Find ƒ ( E ) for je F ( E ) . 9 For any bounded linear operator T show that 10 0 , ( T ) ≤ 0 , ( T ...
Page 600
... spectrum is divided into three disjoint sets : the point spectrum , continuous spectrum and residual spectrum . It is seen from Lemma 2 below that the spectrum is a closed set . But , in contrast to the case where T is a bounded ...
... spectrum is divided into three disjoint sets : the point spectrum , continuous spectrum and residual spectrum . It is seen from Lemma 2 below that the spectrum is a closed set . But , in contrast to the case where T is a bounded ...
Page 612
... spectrum . The con- tinuous spectrum is much more difficult to handle , but has been dis- cussed by Friedrichs [ 1 , 2 ] . Unexpected phenomena can take place under perturbation . For example , Weyl [ 2 ] showed that if T is a self ...
... spectrum . The con- tinuous spectrum is much more difficult to handle , but has been dis- cussed by Friedrichs [ 1 , 2 ] . Unexpected phenomena can take place under perturbation . For example , Weyl [ 2 ] showed that if T is a self ...
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