Linear Operators: Spectral operators |
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Page 2154
... manifolds { x | ( T — \ I ) TM x = 0 } increase with m , it follows that ( T_ \ I ) n + 1 + { x | ( T − AI ) n + xx = 0 } is dense in X. By induction , it is seen that the manifold . ( T − XI ) n + kX + { x | ( T — λI ) n + kx = 0 } ...
... manifolds { x | ( T — \ I ) TM x = 0 } increase with m , it follows that ( T_ \ I ) n + 1 + { x | ( T − AI ) n + xx = 0 } is dense in X. By induction , it is seen that the manifold . ( T − XI ) n + kX + { x | ( T — λI ) n + kx = 0 } ...
Page 2214
... manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra A ( B ) generated by B. Thus W ( B ) A ( B ) . On the other hand , it is clear that A ( B ) ≤ W ( B ) . Q.E.D. The ...
... manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra A ( B ) generated by B. Thus W ( B ) A ( B ) . On the other hand , it is clear that A ( B ) ≤ W ( B ) . Q.E.D. The ...
Page 2270
... manifold in X * containing all the sets A .. ( b ) The projection Fo with range M and null manifold N defined by this decomposition belongs to D. It is easily verified that X - completeness implies completeness for D as an abstract ...
... manifold in X * containing all the sets A .. ( b ) The projection Fo with range M and null manifold N defined by this decomposition belongs to D. It is easily verified that X - completeness implies completeness for D as an abstract ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ 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 operator 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 subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero