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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 Borel function 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 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