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 86
Page 1938
... operator S which is of scalar type in accordance with the follow- ing definition . DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which satisfies the equation S = √ λE ( dλ ) , where E ...
... operator S which is of scalar type in accordance with the follow- ing definition . DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which satisfies the equation S = √ λE ( dλ ) , where E ...
Page 2147
... linear operator T satisfy conditions ( A ) , ( B ) , and ( C ) . Then , by Theorem 3.11 and Lemma 3 , T is a spectral operator of class ( S ( T ) , X * ) with a resolution of the identity which is countably additive in the strong operator ...
... linear operator T satisfy conditions ( A ) , ( B ) , and ( C ) . Then , by Theorem 3.11 and Lemma 3 , T is a spectral operator of class ( S ( T ) , X * ) with a resolution of the identity which is countably additive in the strong operator ...
Page 2162
... linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the conditions ( a ) ...
... linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the conditions ( a ) ...
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