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 |
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Page 1909
... theory of spectral operators in Part II . We thought ( and still think ) that this theory forms an excellent introduction to the detailed study of the much more refined and complete theory of self adjoint operators in Hilbert space . It ...
... theory of spectral operators in Part II . We thought ( and still think ) that this theory forms an excellent introduction to the detailed study of the much more refined and complete theory of self adjoint operators in Hilbert space . It ...
Page 2112
... theory of type 3 if for arbitrary open sets G1 , ... , G , which cover the complex plane , there exist closed linear subspaces M1 , ... , M , which span X , are invariant under T , and such that o ( T | M1 ) ≤ G1 , i = 1 , ... , n ...
... theory of type 3 if for arbitrary open sets G1 , ... , G , which cover the complex plane , there exist closed linear subspaces M1 , ... , M , which span X , are invariant under T , and such that o ( T | M1 ) ≤ G1 , i = 1 , ... , n ...
Page 2227
... theory of Hermitian operators to ordinary and partial differential operators it is first necessary to extend the spectral theory of bounded operators to a theory of unbounded operators . The present chapter is an attempt to make the ...
... theory of Hermitian operators to ordinary and partial differential operators it is first necessary to extend the spectral theory of bounded operators to a theory of unbounded operators . The present chapter is an attempt to make the ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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