Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2200
... projection F in S ( B ) - is in B. The proof that F is in B will be made by showing that to each pair ( y , z ) where У is in M FX and z is in N = ( I — F ) X , there can be asso- ciated a projection E2 in B such that E12y = y = Fy ...
... projection F in S ( B ) - is in B. The proof that F is in B will be made by showing that to each pair ( y , z ) where У is in M FX and z is in N = ( I — F ) X , there can be asso- ciated a projection E2 in B such that E12y = y = Fy ...
Page 2266
... projection of x . ( Note that if G is the carrier projection of x and 0 F≤ G , then Fx 0. ) The cyclic subspace M ( x ) spanned by a vector x is sp { Ex | E = B } . A projection E e B will be said to satisfy the countable chain ...
... projection of x . ( Note that if G is the carrier projection of x and 0 F≤ G , then Fx 0. ) The cyclic subspace M ( x ) spanned by a vector x is sp { Ex | E = B } . A projection E e B will be said to satisfy the countable chain ...
Page 2271
... projection of x 。 is the identity I. Thus if 0 E € B , we have Ex 。 0 , and I satisfies the countable chain condition . It will be con- venient to isolate a portion of the argument . 13 PROPOSITION . If 0 Fe B there exists a projection ...
... projection of x 。 is the identity I. Thus if 0 E € B , we have Ex 。 0 , and I satisfies the countable chain condition . It will be con- venient to isolate a portion of the argument . 13 PROPOSITION . If 0 Fe B there exists a projection ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero