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 2163
... uniform operator topology , and for which ( ii ) F ( § ) T = TF ( § ) , ξεσ ( Τ ) . It is seen from Corollary XV.3.7 ... uniform topology of operators for every function F on σ ( T ) which is continuous in the uniform operator topology ...
... uniform operator topology , and for which ( ii ) F ( § ) T = TF ( § ) , ξεσ ( Τ ) . It is seen from Corollary XV.3.7 ... uniform topology of operators for every function F on σ ( T ) which is continuous in the uniform operator topology ...
Page 2265
... uniform multiplicity n . - Є PROOF . We show first that each nonzero E B bounds a nonzero Ge B of uniform multiplicity . Let no = min { m ( F ) | 0 F≤ E } . Since the cardinals are well ordered , there exists a projection GE with m ( G ) ...
... uniform multiplicity n . - Є PROOF . We show first that each nonzero E B bounds a nonzero Ge B of uniform multiplicity . Let no = min { m ( F ) | 0 F≤ E } . Since the cardinals are well ordered , there exists a projection GE with m ( G ) ...
Page 2283
... uniform 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 ...
... uniform 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 ...
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