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 91
Page 2209
... closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed algebra ...
... closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed algebra ...
Page 2214
... closed operator algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant ...
... closed operator algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant ...
Page 2217
... closed linear manifolds generated by the sets { ExE = B } , { Ex | E e B1 } , respectively . Since B1 is the strong closure of B , each element Ex with E in ... closed operator algebra generated by B ) XVII.3.24 2217 STRONGLY CLOSED ALGEBRAS.
... closed linear manifolds generated by the sets { ExE = B } , { Ex | E e B1 } , respectively . Since B1 is the strong closure of B , each element Ex with E in ... closed operator algebra generated by B ) XVII.3.24 2217 STRONGLY CLOSED ALGEBRAS.
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero