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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Results 1-3 of 18
Page 2320
... equal to m , and Ď having order at most equal to m – 1. If B and Ĉ do actually both have order m , then , subtracting a suitable multiple of B from C , and a suitable multiple of Ĉ from B , we find an equivalent set of three boundary ...
... equal to m , and Ď having order at most equal to m – 1. If B and Ĉ do actually both have order m , then , subtracting a suitable multiple of B from C , and a suitable multiple of Ĉ from B , we find an equivalent set of three boundary ...
Page 2343
... equal to the product ( iw 。) m1 ( iw1 ) m1 ... ( iw , -1 ) m1 m2 ( iw 。) TM 2 ... ( iwo ) my ... X μ ( iw , -1 ) mv e - 1 " ( iw , ) mv + 1 ( iwv + 1 ) mv + 1 - tu ( iw1 ) mv + 2 ( iwy + 1 ) mv + 2 ... e - iu ( iw , ) m2v ( iwy +1 ) ...
... equal to the product ( iw 。) m1 ( iw1 ) m1 ... ( iw , -1 ) m1 m2 ( iw 。) TM 2 ... ( iwo ) my ... X μ ( iw , -1 ) mv e - 1 " ( iw , ) mv + 1 ( iwv + 1 ) mv + 1 - tu ( iw1 ) mv + 2 ( iwy + 1 ) mv + 2 ... e - iu ( iw , ) m2v ( iwy +1 ) ...
Page 2365
... equals C , proving by Definition 2.1 that TP is discrete . - = Since by hypothesis D ( T - 1P ) ≥ D ( T ' ) for l≤k ... equal to R ( μi ; T ) * ( I + Oμ ) −1 . This shows , in particular , that D ( ( T + P ) * ) ≤ D ( T ) , so that D ...
... equals C , proving by Definition 2.1 that TP is discrete . - = Since by hypothesis D ( T - 1P ) ≥ D ( T ' ) for l≤k ... equal to R ( μi ; T ) * ( I + Oμ ) −1 . This shows , in particular , that D ( ( T + P ) * ) ≤ D ( T ) , so that D ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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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