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 2264
... Multiplicity Theory and Spectral Representation The methods and results of this section are due to Bade and are intimately dependent upon the ideas introduced in Section XVII.3 . A multiplicity theory for Boolean algebras of projections ...
... Multiplicity Theory and Spectral Representation The methods and results of this section are due to Bade and are intimately dependent upon the ideas introduced in Section XVII.3 . A multiplicity theory for Boolean algebras of projections ...
Page 2265
... multiplicity function on B which is an extension of m on D. α PROOF . If E E B define m ( E ) = Vam ( Ba ) , where { B } is any family . in D such that E = \ / B. If ... multiplicity function for B it will XVIII.3.2 2265 MULTIPLICITY THEORY.
... multiplicity function on B which is an extension of m on D. α PROOF . If E E B define m ( E ) = Vam ( Ba ) , where { B } is any family . in D such that E = \ / B. If ... multiplicity function for B it will XVIII.3.2 2265 MULTIPLICITY THEORY.
Page 2283
... multiplicity n if and only if its adjoint E * in B * has finite uniform multiplicity n . PROOF . It is sufficient to suppose E and E * satisfy the countable chain condition . Also since each projection is the union of projections of ...
... multiplicity n if and only if its adjoint E * in B * has finite uniform multiplicity n . PROOF . It is sufficient to suppose E and E * satisfy the countable chain condition . Also since each projection is the union of projections of ...
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