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 1921
... SPECTRAL OPERATORS XV . Spectral Operators 1 . Introduction 2. Terminology and Preliminary Notions 3. The Resolvent of a Spectral Operator 4. The Canonical Reduction of a Spectral Operator 5. An Operational Calculus for Bounded Spectral ...
... SPECTRAL OPERATORS XV . Spectral Operators 1 . Introduction 2. Terminology and Preliminary Notions 3. The Resolvent of a Spectral Operator 4. The Canonical Reduction of a Spectral Operator 5. An Operational Calculus for Bounded Spectral ...
Page 2169
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for ... spectral measure which , in view of the Orlicz - Pettis Theorem IV.10.1 , is countably additive in the strong operator ...
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for ... spectral measure which , in view of the Orlicz - Pettis Theorem IV.10.1 , is countably additive in the strong operator ...
Page 2228
... bounded ; E ( o ) D ( T ) ≤ D ( T ) TE ( o ) x = E ( 0 ) Tx , xED ( T ) , σ EB ; ( iii ) the restriction T | E ( o ) X with domain D ( T ) ~ E ( σ ) X has its ... spectral operator with 2228 XVIII.2.1 XVIII . UNBOUNDED SPECTRAL OPERATORS.
... bounded ; E ( o ) D ( T ) ≤ D ( T ) TE ( o ) x = E ( 0 ) Tx , xED ( T ) , σ EB ; ( iii ) the restriction T | E ( o ) X with domain D ( T ) ~ E ( σ ) X has its ... spectral operator with 2228 XVIII.2.1 XVIII . UNBOUNDED SPECTRAL OPERATORS.
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