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 1974
... implies ( iii ) . It is clear that ( iii ) implies ( i ) , and so to prove the lemma it will suffice to prove that ( i ) implies ( ii ) . Let ( a ) sup e - ess sup E ( o ; T ( s ) ) | = K < ∞ , σε SES and suppose that for some i GS ...
... implies ( iii ) . It is clear that ( iii ) implies ( i ) , and so to prove the lemma it will suffice to prove that ( i ) implies ( ii ) . Let ( a ) sup e - ess sup E ( o ; T ( s ) ) | = K < ∞ , σε SES and suppose that for some i GS ...
Page 2174
... implies that the bounded group G = { ett te R } is equivalent to a group of unitary operators . By Stone's theorem ... imply that T is spectral , even when X is reflexive . To see this , note that if S and T are commuting scalar ...
... implies that the bounded group G = { ett te R } is equivalent to a group of unitary operators . By Stone's theorem ... imply that T is spectral , even when X is reflexive . To see this , note that if S and T are commuting scalar ...
Page 2218
... implies strong convergence . 27 THEOREM . If a generalized sequence of projections in a o - complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly . - α PROOF . In view of ...
... implies strong convergence . 27 THEOREM . If a generalized sequence of projections in a o - complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly . - α PROOF . In view of ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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