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 2021
... equation Ap = 0 , being equivalent to the Cauchy - Riemann equation for the real and imaginary parts of a holomorphic function , has no non - zero solution y in 2. For , by classical function theory , any solution = ( 91 , 92 ) in Ø2 of ...
... equation Ap = 0 , being equivalent to the Cauchy - Riemann equation for the real and imaginary parts of a holomorphic function , has no non - zero solution y in 2. For , by classical function theory , any solution = ( 91 , 92 ) in Ø2 of ...
Page 2074
... equation ( 36 ) . Then ( 31 ) shows that x is in H + and equation ( 35 ) holds . This means that for some vector z in H. we have - - et ( 9 ) y = e − 3 e − 3 ( 9 + ) x + 2 , and , using ( 30 ) , it is seen that - = y = ax + e - 5 ( 9 ...
... equation ( 36 ) . Then ( 31 ) shows that x is in H + and equation ( 35 ) holds . This means that for some vector z in H. we have - - et ( 9 ) y = e − 3 e − 3 ( 9 + ) x + 2 , and , using ( 30 ) , it is seen that - = y = ax + e - 5 ( 9 ...
Page 2401
... equation ( 1 ) is equivalent to the equation ( 2 ) that is , to ( 3 ) ( I + T ( B ) ) ( T + 9 ( A1 ) ) = T ( I + T ( B ) ) , T ( B ) T — TT ( B ) = −T ( B ) q ( A1 ) — ( A1 ) , q ( B ) — T ( B ) q ( A1 ) = q ( A1 ) . or , using ...
... equation ( 1 ) is equivalent to the equation ( 2 ) that is , to ( 3 ) ( I + T ( B ) ) ( T + 9 ( A1 ) ) = T ( I + T ( B ) ) , T ( B ) T — TT ( B ) = −T ( B ) q ( A1 ) — ( A1 ) , q ( B ) — T ( B ) q ( A1 ) = q ( A1 ) . or , using ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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 invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian 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