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 1956
... fact and Theorem 2 it follows that À is not in o , ( T ) . The final argument of the theorem shows that ( AIT ) is dense in X and hence , since À is in o ( T ) , it must be in σ ( T ) . This proves the second inclusion , and the final ...
... fact and Theorem 2 it follows that À is not in o , ( T ) . The final argument of the theorem shows that ( AIT ) is dense in X and hence , since À is in o ( T ) , it must be in σ ( T ) . This proves the second inclusion , and the final ...
Page 2056
... facts which allows the man to recover only if he calls a physician . These two facts , that of recovering and that of ... fact that man is an incontinent being . Thus man's decisions , which affect his actions and thus determine his ...
... facts which allows the man to recover only if he calls a physician . These two facts , that of recovering and that of ... fact that man is an incontinent being . Thus man's decisions , which affect his actions and thus determine his ...
Page 2205
... fact will be unimportant in what follows . An appli- cation of Zorn's lemma yields a maximal family { S } of disjoint sets each of which is a y - carrier for some y * in X * . It will first be observed that { 8 } is at most denumerable ...
... fact will be unimportant in what follows . An appli- cation of Zorn's lemma yields a maximal family { S } of disjoint sets each of which is a y - carrier for some y * in X * . It will first be observed that { 8 } is at most denumerable ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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 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