Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 31
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 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 ...
Page 2289
... multiplicity when E has infinite uniform multiplicity . A related question concerns invariant subspaces . If M is an invariant subspace we may define the multiplicity of B in M. If M1 ≤ M2 it is to be expected that m1 ( E ) ≤ m2 ( E ) ...
... multiplicity when E has infinite uniform multiplicity . A related question concerns invariant subspaces . If M is an invariant subspace we may define the multiplicity of B in M. If M1 ≤ M2 it is to be expected that m1 ( E ) ≤ m2 ( E ) ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero