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 38
Page 2154
... manifolds { x | ( T — \ I ) TM x = 0 } increase with m , it follows that - - ( T — \ I ) n + 1X + { x | ( T — λI ) n + 1x = 0 } is dense in X. By induction , it is seen that the manifold --- ( T_ \ I ) n + k ¥ + { \ ( T _ \\ n + kx = 0 } ...
... manifolds { x | ( T — \ I ) TM x = 0 } increase with m , it follows that - - ( T — \ I ) n + 1X + { x | ( T — λI ) n + 1x = 0 } is dense in X. By induction , it is seen that the manifold --- ( T_ \ I ) n + k ¥ + { \ ( T _ \\ n + kx = 0 } ...
Page 2214
... manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra ( B ) generated by B. Thus W ( B ) A ( B ) . On the other hand , it is clear that A ( B ) ≤ W ( B ) . Q.E.D. The preceding ...
... manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra ( B ) generated by B. Thus W ( B ) A ( B ) . On the other hand , it is clear that A ( B ) ≤ W ( B ) . Q.E.D. The preceding ...
Page 2270
... manifold in X * containing all the sets A。· ( b ) The projection Fo with range M and null manifold N defined by this decomposition belongs to D. It is easily verified that X - completeness implies completeness for D as an abstract ...
... manifold in X * containing all the sets A。· ( b ) The projection Fo with range M and null manifold N defined by this decomposition belongs to D. It is easily verified that X - completeness implies completeness for D as an abstract ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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