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 2047
... to r argument ( u remains away from zero . In view of Theorem III.6.20 equation ( 93 ) may be written as d ( 94 ) dě · Sn . r ( 5 ) q = rT1 ( 5 — r§ ) BSn − 1 ( r§ ) q with r < 1 , the τζ + A。[ " T ̧ ( 5 — u ) BS , - 1 ( u ) q du . 0 ...
... to r argument ( u remains away from zero . In view of Theorem III.6.20 equation ( 93 ) may be written as d ( 94 ) dě · Sn . r ( 5 ) q = rT1 ( 5 — r§ ) BSn − 1 ( r§ ) q with r < 1 , the τζ + A。[ " T ̧ ( 5 — u ) BS , - 1 ( u ) q du . 0 ...
Page 2220
... and R ( A ; Ta ) . Thus , since the product of bounded , strongly convergent generalized sequences is itself a ... on R ( V ) has a unique continuous extension to a homomorphism of C ( V ) onto the uniformly closed operator algebra ...
... and R ( A ; Ta ) . Thus , since the product of bounded , strongly convergent generalized sequences is itself a ... on R ( V ) has a unique continuous extension to a homomorphism of C ( V ) onto the uniformly closed operator algebra ...
Page 2365
... ( R ( ui ; T ) ) has norm less than 1 , then the operator ( ( μil — T — P ) * ) -1 exists and is equal to R ( μi ; T ) * ( I + Oμ ) −1 . This shows , in particular , that D ( ( T + P ) * ) ≤ D ( T ) , so that D ( ( T + P ) * ) = D ( T ) ...
... ( R ( ui ; T ) ) has norm less than 1 , then the operator ( ( μil — T — P ) * ) -1 exists and is equal to R ( μi ; T ) * ( I + Oμ ) −1 . This shows , in particular , that D ( ( T + P ) * ) ≤ D ( T ) , so that D ( ( T + P ) * ) = D ( T ) ...
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