Linear Operators, Part 2 |
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Results 1-3 of 67
Page 1936
... restriction TEX is the corresponding restriction of the resolution of the identity for T. PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( σ ; T ) in the resolution of the identity for T. It ...
... restriction TEX is the corresponding restriction of the resolution of the identity for T. PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( σ ; T ) in the resolution of the identity for T. It ...
Page 2094
... restriction T | Y of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace of ...
... restriction T | Y of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace of ...
Page 2228
... restriction TE ( o ) x with domain D ( T ) E ( o ) has its spectrum o ( T | E ( 0 ) X ) ≤ ō , σ € B. The spectral ... restriction T | E ( o ) X of T to E ( o ) X is a spectral operator whose resolution of the identity is the restriction ...
... restriction TE ( o ) x with domain D ( T ) E ( o ) has its spectrum o ( T | E ( 0 ) X ) ≤ ō , σ € B. The spectral ... restriction T | E ( o ) X of T to E ( o ) X is a spectral operator whose resolution of the identity is the restriction ...
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