Linear Operators, Part 2 |
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Page 2160
... shown that the vector x y is in the closure of the manifold ( I − T ) 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 ...
... shown that the vector x y is in the closure of the manifold ( I − T ) 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 ...
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 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 if and only if it is the ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero