Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 76
Page 1948
... commutes with A * . PROOF . This is a corollary of Corollary 3.7 . Q.E.D. 2 PROOF OF COROLLARY 5. Let T1 , T2 be commuting spectral operators in Hilbert space 5 and let S1 + N1 , S2 + N2 be their canonical decomposi- tions . It follows ...
... commutes with A * . PROOF . This is a corollary of Corollary 3.7 . Q.E.D. 2 PROOF OF COROLLARY 5. Let T1 , T2 be commuting spectral operators in Hilbert space 5 and let S1 + N1 , S2 + N2 be their canonical decomposi- tions . It follows ...
Page 2098
... commuting quasi - nilpotent . Spectral operators in Hilbert space . The fact that a finite number of commuting spectral operators in a Hilbert space can be simultaneously transformed into normal operators by passing to an equivalent ...
... commuting quasi - nilpotent . Spectral operators in Hilbert space . The fact that a finite number of commuting spectral operators in a Hilbert space can be simultaneously transformed into normal operators by passing to an equivalent ...
Page 2177
... commuting spectral operators in Hilbert space . The attentive reader may have noticed , however , that no attempt ... commuting spectral operators be spectral . At the same time , various sufficient conditions that the uniform , weak ...
... commuting spectral operators in Hilbert space . The attentive reader may have noticed , however , that no attempt ... commuting spectral operators be spectral . At the same time , various sufficient conditions that the uniform , weak ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
36 other sections not shown
Other editions - View all
Common terms and phrases
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