Linear Operators: Spectral operators |
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Page 2160
... shown that the vector x y is in the closure of the manifold ( IT ) X . To see this it will , in view of Corollary II.3.13 , suffice to show that x * ( x − y ) = 0 for every linear functional x * which vanishes on ( I − T ) X . If x ...
... shown that the vector x y is in the closure of the manifold ( IT ) X . To see this it will , in view of Corollary II.3.13 , suffice to show that x * ( x − y ) = 0 for every linear functional x * which vanishes on ( I − T ) X . If x ...
Page 2226
... shown that in a complete metrizable locally convex space there may not be a single functional corresponding to x ... shown by a counterexample constructed by C. Foias . Berkson [ 5 ] has shown that this hypothesis is satisfied if the ...
... shown that in a complete metrizable locally convex space there may not be a single functional corresponding to x ... shown by a counterexample constructed by C. Foias . Berkson [ 5 ] has shown that this hypothesis is satisfied if the ...
Page 2266
... shown that is a dense σ - ideal in B and thus , in defining the multiplicity on B , Lemma 2 permits us to restrict our attention to C. 5 LEMMA . The set C is a dense o - ideal in B. A projection belongs to 6 if and only if it is the ...
... shown that is a dense σ - ideal in B and thus , in defining the multiplicity on B , Lemma 2 permits us to restrict our attention to C. 5 LEMMA . The set C is a dense o - ideal in B. A projection belongs to 6 if and only if it is the ...
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