Linear Operators: Spectral operators |
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Page 2163
... uniform operator topology , and for which ( ii ) F ( ¿ ) T = TF ( § ) , હું ૯ ( T ) . It is seen from Corollary ... 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 ( § ) , હું ૯ ( T ) . It is seen from Corollary ... uniform topology of operators for every function F on σ ( T ) which is continuous in the uniform operator topology ...
Page 2265
... uniform multiplicity n . Ꮐ 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 G≤ E with ...
... uniform multiplicity n . Ꮐ 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 G≤ E with ...
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero