Linear Operators: Spectral operators |
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Page 2095
... operator T is spectral if and only if the restriction TV is spectral . Consequently , the analogs of the results stated in the preceding paragraph for restrictions of spectral and scalar type operators also hold for their quotients ...
... operator T is spectral if and only if the restriction TV is spectral . Consequently , the analogs of the results stated in the preceding paragraph for restrictions of spectral and scalar type operators also hold for their quotients ...
Page 2106
... scalar type operator of class ( X ) , and ( ii ) if X is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and is weakly complete , then A is scalar type if and only if either ( a ) A is invertible ...
... scalar type operator of class ( X ) , and ( ii ) if X is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and is weakly complete , then A is scalar type if and only if either ( a ) A is invertible ...
Page 2174
... operator - valued function defined on rectangles . In a Hilbert space the condition that lett≤ M for all t e R implies that T is equivalent to a self adjoint operator and hence is a scalar type operator with real spectrum . ( This ...
... operator - valued function defined on rectangles . In a Hilbert space the condition that lett≤ M for all t e R implies that T is equivalent to a self adjoint operator and hence is a scalar type operator with real spectrum . ( This ...
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