Linear Operators: Spectral operators |
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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. Foiaş . 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. Foiaş . Berkson [ 5 ] has shown that this hypothesis is satisfied if the ...
Page 2246
... shown in precisely the same way that if J is a subset of the class of positive integers , and HJ = ΣneJ → H ( n ) , then the spectrum of the restriction CS , is J. Since ( iI - C ) -1 is bounded , il -C is closed . Thus C is closed ...
... shown in precisely the same way that if J is a subset of the class of positive integers , and HJ = ΣneJ → H ( n ) , then the spectrum of the restriction CS , is J. Since ( iI - C ) -1 is bounded , il -C is closed . Thus C is closed ...
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 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 is a dense o - ideal in B. A projection belongs to 6 if and only if it is the ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero