Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2011
... defined almost everywhere on S but not necessarily bounded . For every set σ in E and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined ...
... defined almost everywhere on S but not necessarily bounded . For every set σ in E and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined ...
Page 2018
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( AI - Ag ) -1 exists as a bounded everywhere defined operator . The spectrum σ ( A ) of Ag is defined to be the complement p ( A ) . It is clear from the ...
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( AI - Ag ) -1 exists as a bounded everywhere defined operator . The spectrum σ ( A ) of Ag is defined to be the complement p ( A ) . It is clear from the ...
Page 2284
... defined and continuous , and the map An W1T is a densely defined closed map of E , X into H , with densely defined inverse . We suppose the norm of [ h1 , hn ] in 5 , is defined to be = n n n 1 , ... , [ £ Σιδα ( 1 ) μιαλ ) = 1 P 1/2 so ...
... defined and continuous , and the map An W1T is a densely defined closed map of E , X into H , with densely defined inverse . We suppose the norm of [ h1 , hn ] in 5 , is defined to be = n n n 1 , ... , [ £ Σιδα ( 1 ) μιαλ ) = 1 P 1/2 so ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ 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