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 2092
... equivalent ; the general notion extends this case . ) The relation of being quasi - nilpotent equivalent is indeed an equivalence relation and , when T and U are quasi - nilpotent equivalent , then ( i ) σ ( T ) = σ ( U ) , ( ii ) T has ...
... equivalent ; the general notion extends this case . ) The relation of being quasi - nilpotent equivalent is indeed an equivalence relation and , when T and U are quasi - nilpotent equivalent , then ( i ) σ ( T ) = σ ( U ) , ( ii ) T has ...
Page 2105
... equivalent to | · | and relative to which all the operators E ( S ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then || ƒ ƒ ( 8 ) E ( ds ) || = sup | ƒ ( 8 ) ...
... equivalent to | · | and relative to which all the operators E ( S ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then || ƒ ƒ ( 8 ) E ( ds ) || = sup | ƒ ( 8 ) ...
Page 2115
... equivalent , then U is a spectral operator . Moreover , if T and U are spectral , then they are quasi - nilpotent equivalent if and only if they have the same resolution of the identity , and if and only if the single condition : lim ...
... equivalent , then U is a spectral operator . Moreover , if T and U are spectral , then they are quasi - nilpotent equivalent if and only if they have the same resolution of the identity , and if and only if the single condition : lim ...
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