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 2300
... uniformly bounded . Moreover , Σ- , ( E ( \ , ; T ) — E ( un ; T + P ) ) clearly converges uniformly for p≥ K and approaches zero in norm as p → ∞o . Since E , EA ; T ) converges strongly ( T being spectral ) , it follows that the ...
... uniformly bounded . Moreover , Σ- , ( E ( \ , ; T ) — E ( un ; T + P ) ) clearly converges uniformly for p≥ K and approaches zero in norm as p → ∞o . Since E , EA ; T ) converges strongly ( T being spectral ) , it follows that the ...
Page 2361
... uniformly bounded for λ in UN V1 , and hence , by the maximum modulus theorem , is uniformly bounded for A in UN U .. Since the set { U1 } , i ≥ N , covers the whole plane , with the possible excep- tion of a bounded set , | F * ( A ) ...
... uniformly bounded for λ in UN V1 , and hence , by the maximum modulus theorem , is uniformly bounded for A in UN U .. Since the set { U1 } , i ≥ N , covers the whole plane , with the possible excep- tion of a bounded set , | F * ( A ) ...
Page 2382
... uniformly for μ € P + and 0 ≤t < ∞o . On the other hand , integrating by parts , we see that for each n 1 ∞ e2tu ( s - t ) qn ( s ) ds 1 ∞ = In ( t ) 2iμ 2iμ ན ། e2tu ( s - tq ( s ) dt → 0 as μ → ∞ , μ ε P + , uniformly in 0 ...
... uniformly for μ € P + and 0 ≤t < ∞o . On the other hand , integrating by parts , we see that for each n 1 ∞ e2tu ( s - t ) qn ( s ) ds 1 ∞ = In ( t ) 2iμ 2iμ ན ། e2tu ( s - tq ( s ) dt → 0 as μ → ∞ , μ ε P + , uniformly in 0 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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 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