Linear Operators: Spectral operators |
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Page 2068
... contains all inverses . There are a number of immediate corollaries to this theorem of Wiener which will become apparent from the following lemma . 6 LEMMA . Let I be an ideal in the subalgebra A。 of A and let A ( J ) be the algebra of ...
... contains all inverses . There are a number of immediate corollaries to this theorem of Wiener which will become apparent from the following lemma . 6 LEMMA . Let I be an ideal in the subalgebra A。 of A and let A ( J ) be the algebra of ...
Page 2069
... contains all inverses . Then Ag contains all inverses . 1 PROOF . If the operator A in Ag has an inverse in B ( 5 " ) then , by Corollary 9.6 , A - 1 is in " and the determinant & = det ( a ,, ) has an inverse in A. Since A。 contains ...
... contains all inverses . Then Ag contains all inverses . 1 PROOF . If the operator A in Ag has an inverse in B ( 5 " ) then , by Corollary 9.6 , A - 1 is in " and the determinant & = det ( a ,, ) has an inverse in A. Since A。 contains ...
Page 2159
... contains a non - trivial sub- interval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T * contains no non - trivial subarc of To , then the set of points regular relative to T is dense in à 。· PROOF . If is not in ...
... contains a non - trivial sub- interval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T * contains no non - trivial subarc of To , then the set of points regular relative to T is dense in à 。· PROOF . If is not in ...
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