Linear Operators: Spectral operators |
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Page 1926
... arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E defined by the equations N - TXE ( X ) , E ( 8 ) ...
... arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E defined by the equations N - TXE ( X ) , E ( 8 ) ...
Page 1941
... arbitrary , it follows that o ( N ) = { 0 } . It then follows from Corollary 3 that N is a quasi - nilpotent . Q.E.D. 6 DEFINITION . The decomposition , given in Theorem 5 , of a spectral operator TS + N into a sum of a scalar type ...
... arbitrary , it follows that o ( N ) = { 0 } . It then follows from Corollary 3 that N is a quasi - nilpotent . Q.E.D. 6 DEFINITION . The decomposition , given in Theorem 5 , of a spectral operator TS + N into a sum of a scalar type ...
Page 2193
... arbitrary B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then ...
... arbitrary B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then ...
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