Linear Operators: Spectral operators |
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Page 2296
... discrete operator . The space all f in X for which ( T — XI ) − 1f is an entire function of X. ∞ ( T ) is the set of PROOF . If ( T - XI ) - 1ƒ is entire , then by letting C be a small circle around λ , e σ ( T ) we find that 0 1 2 ...
... discrete operator . The space all f in X for which ( T — XI ) − 1f is an entire function of X. ∞ ( T ) is the set of PROOF . If ( T - XI ) - 1ƒ is entire , then by letting C be a small circle around λ , e σ ( T ) we find that 0 1 2 ...
Page 2362
... discrete and ( TB ) = 0 . PROOF . This follows from Theorem 6 by placing v = 0 . Q.E.D. 9 COROLLARY . Let T be a discrete spectral operator in the reflexive B - space X. Suppose that all but a finite number of the points in o ( T ...
... discrete and ( TB ) = 0 . PROOF . This follows from Theorem 6 by placing v = 0 . Q.E.D. 9 COROLLARY . Let T be a discrete spectral operator in the reflexive B - space X. Suppose that all but a finite number of the points in o ( T ...
Page 2448
... discrete spectrum , and even for application to operators with mixed discrete and continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due to Robert E. L. Turner , concerning ...
... discrete spectrum , and even for application to operators with mixed discrete and continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due to Robert E. L. Turner , concerning ...
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