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 1965
... algebra C ( S ) of all bounded continuous complex functions on S as a B * -subalgebra of eB ( S , Σ ) , for if e ( 8 ) ... algebra  . In case  is such an algebra of continuous functions , we shall sometimes write C instead of A for the ...
... algebra C ( S ) of all bounded continuous complex functions on S as a B * -subalgebra of eB ( S , Σ ) , for if e ( 8 ) ... algebra  . In case  is such an algebra of continuous functions , we shall sometimes write C instead of A for the ...
Page 2194
... algebra of all operators of the form Sƒ ( A ) E ( dλ ) where ƒ is E - essentially bounded on o ( S ) . It follows from Theorem 10 that A1 is a full algebra of scalar type spectral operators which is equivalent to EB ( A , E ) . It ...
... algebra of all operators of the form Sƒ ( A ) E ( dλ ) where ƒ is E - essentially bounded on o ( S ) . It follows from Theorem 10 that A1 is a full algebra of scalar type spectral operators which is equivalent to EB ( A , E ) . It ...
Page 2214
... algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant every closed linear ...
... algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant every closed linear ...
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