Linear Operators, Part 2 |
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Page 2283
... finite 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 ...
... finite 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 ...
Page 2292
... finite limit point ; ( b ) the resolvent R ( A ; T ) is compact for every & σ ( T ) ; λ ( c ) every λ 。 in o ( T ) is a pole of finite order v ( λ ) of the resolvent and if , for some positive integer k , f satisfies the equation then ...
... finite limit point ; ( b ) the resolvent R ( A ; T ) is compact for every & σ ( T ) ; λ ( c ) every λ 。 in o ( T ) is a pole of finite order v ( λ ) of the resolvent and if , for some positive integer k , f satisfies the equation then ...
Page 2469
... finite , and that | V * < e . Thus the proof of our lemma is complete . Q.E.D. ― Next we prove an important inequality . 17 LEMMA . Suppose that we call on element ƒ H ' very smooth and finite if ( i ) there exists an integer n such ...
... finite , and that | V * < e . Thus the proof of our lemma is complete . Q.E.D. ― Next we prove an important inequality . 17 LEMMA . Suppose that we call on element ƒ H ' very smooth and finite if ( i ) there exists an integer n such ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 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