Linear Operators, Part 2 |
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Page 2403
... apply Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ...
... apply Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ...
Page 2418
... apply Theorem 8 and Corollary 9 , and the conclusion of the present theorem follows immediately . Q.E.D. As the ... application of Theorems 2418 SPECTRAL OPERATORS WITH CONTINUOUS SPECTRA XX.2.10.
... apply Theorem 8 and Corollary 9 , and the conclusion of the present theorem follows immediately . Q.E.D. As the ... application of Theorems 2418 SPECTRAL OPERATORS WITH CONTINUOUS SPECTRA XX.2.10.
Page 2498
... apply the Kato - Kuroda theorem to relate the spectra of S and S1 . 1 The circle of ideas described in Section 4 was ... application of this inequality to prove the general Theorem 4.9 is due to Kato [ 9 , 10 ] . The extension to ...
... apply the Kato - Kuroda theorem to relate the spectra of S and S1 . 1 The circle of ideas described in Section 4 was ... application of this inequality to prove the general Theorem 4.9 is due to Kato [ 9 , 10 ] . The extension to ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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