Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 46
Page 2154
... interval of constancy relative to T is a non - void open subinterval of à ̧ upon which some index function for T is constant . A point λ in T。 is said to be regular relative to T if it belongs to an interval of constancy and if , in ...
... interval of constancy relative to T is a non - void open subinterval of à ̧ upon which some index function for T is constant . A point λ in T。 is said to be regular relative to T if it belongs to an interval of constancy and if , in ...
Page 2159
... 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 the point spectrum of the ...
... 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 the point spectrum of the ...
Page 2160
... interval of constancy relative to T consists entirely of regular points . 0 PROOF . In view of Lemma 11 it suffices to show that a point λ 。 in an interval of constancy relative to T is regular . Since o ( T * ) = σ ( T ) and R ( λ ; T ...
... interval of constancy relative to T consists entirely of regular points . 0 PROOF . In view of Lemma 11 it suffices to show that a point λ 。 in an interval of constancy relative to T is regular . Since o ( T * ) = σ ( T ) and R ( λ ; T ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
35 other sections not shown
Other editions - View all
Common terms and phrases
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