Linear Operators: Spectral operators |
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Page 2256
... compact spectral sets of T is uniformly bounded , and ( b ) no non - zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. 1 PROOF . Suppose first that ( a ) and ( b ) are satisfied . Since σ ( T ) is ...
... compact spectral sets of T is uniformly bounded , and ( b ) no non - zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. 1 PROOF . Suppose first that ( a ) and ( b ) are satisfied . Since σ ( T ) is ...
Page 2357
... compact if P ( T - I ) is compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) , ( c ) of the theorem , we may consequently pass from consideration of the operators T and T + P to consideration of the operators S and S + ( N + P ) ...
... compact if P ( T - I ) is compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) , ( c ) of the theorem , we may consequently pass from consideration of the operators T and T + P to consideration of the operators S and S + ( N + P ) ...
Page 2360
... compact . From this , ( iii ) , and Theorem VI.5.4 , it will follow that B ( μ ) Ru ; T + P ) is compact for μ in V , and i sufficiently large , so that the theorem will be proved . i = Let μ be in V. To show that | T'R ( μ ; T ) A ...
... compact . From this , ( iii ) , and Theorem VI.5.4 , it will follow that B ( μ ) Ru ; T + P ) is compact for μ in V , and i sufficiently large , so that the theorem will be proved . i = Let μ be in V. To show that | T'R ( μ ; T ) A ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operators Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero