Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 94
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 = 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 = 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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
35 other sections not shown
Other editions - View all
Common terms and phrases
A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero