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 2095
... scalar type operators also hold for their quotients . Although the restrictions of operators with the single valued extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed ...
... scalar type operators also hold for their quotients . Although the restrictions of operators with the single valued extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed ...
Page 2106
... scalar type operator of class ( X ) , and ( ii ) if X is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and x is weakly complete , then A is scalar type if and only if either ( a ) A is ...
... scalar type operator of class ( X ) , and ( ii ) if X is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and x is weakly complete , then A is scalar type if and only if either ( a ) A is ...
Page 2174
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { ett | t = R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { ett | t = R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ 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