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 |
From inside the book
Results 1-3 of 71
Page 1930
... countably additive . However , in Corollary X.2.4 we have seen that a bounded normal operator in Hilbert space always has a uniquely defined bounded and countably additive . resolution of the identity defined on the field of all Borel ...
... countably additive . However , in Corollary X.2.4 we have seen that a bounded normal operator in Hilbert space always has a uniquely defined bounded and countably additive . resolution of the identity defined on the field of all Borel ...
Page 1931
... countably additive spectral measure E is a o - field , then E is countably additive in the strong operator topology and bounded . The boundedness of E ( σ ) follows from Corollaries IV.10.2 and II.3.21 . The spectral operators in the ...
... countably additive spectral measure E is a o - field , then E is countably additive in the strong operator topology and bounded . The boundedness of E ( σ ) follows from Corollaries IV.10.2 and II.3.21 . The spectral operators in the ...
Page 2144
... countably additive in the topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) = A ( od ) . It is seen , by using the above remarks , that for a fixed σ the family of 8 for which the equation is valid is a σ ...
... countably additive in the topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) = A ( od ) . It is seen , by using the above remarks , that for a fixed σ the family of 8 for which the equation is valid is a σ ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
23 other sections not shown
Other editions - View all
Common terms and phrases
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