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 but not necessarily bounded . For every set o in Σ and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined operator ...
... defined almost everywhere on but not necessarily bounded . For every set o in Σ and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined operator ...
Page 2018
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( λI — A ̧ ) ̄1 exists as a bounded everywhere defined operator . The spectrum σ ( A ̧ ) of A 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 ( λI — A ̧ ) ̄1 exists as a bounded everywhere defined operator . The spectrum σ ( A ̧ ) of A is defined to be the complement p ( A ) . It is clear from the ...
Page 2284
... defined on the Borel sets of the plane P are positive and vanish outside en . Moreover , there is a natural continuous linear map Tn of Ex into Σî = 1 L1 ( P , B , μ , ) with densely defined inverse . Let Wn denote the identity map of 5 ...
... defined on the Borel sets of the plane P are positive and vanish outside en . Moreover , there is a natural continuous linear map Tn of Ex into Σî = 1 L1 ( P , B , μ , ) with densely defined inverse . Let Wn denote the identity map of 5 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero