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 € B define m ( E ) = \ a m ( 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 € B define m ( E ) = \ a m ( 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 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero