Linear Operators: Spectral operators |
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Page 1936
... identity for the restriction T | EX is the corresponding restriction of the resolution of the identity for T. i PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( σ ; T ) in the resolution of ...
... identity for the restriction T | EX is the corresponding restriction of the resolution of the identity for T. i PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( σ ; T ) in the resolution of ...
Page 2094
... identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where *** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( I ) , then T has a unique ...
... identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where *** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( I ) , then T has a unique ...
Page 2242
... identity for T in the sense of Definition 12 is the same as the resolution of the identity for T in the sense of Definition 1 . PROOF . Using the notations of Definitions 12 and 1 , let T and E have all the properties of Definition 12 ...
... identity for T in the sense of Definition 12 is the same as the resolution of the identity for T in the sense of Definition 1 . PROOF . Using the notations of Definitions 12 and 1 , let T and E have all the properties of Definition 12 ...
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