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 2094
... moreover , if T * is spectral of class ( I ) where ≤ x ** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( Ã ) , then T has a unique resolution of the identity of ...
... moreover , if T * is spectral of class ( I ) where ≤ x ** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( Ã ) , then T has a unique resolution of the identity of ...
Page 2106
... Moreover , if A is adjoint Abelian and X is weakly complete , then A is scalar type if and only if either ( a ) A is invertible , ( b ) 0 is an isolated point of o ( A ) , or ( c ) σ ( A ) is non - negative ( or non - positive ) . It is ...
... Moreover , if A is adjoint Abelian and X is weakly complete , then A is scalar type if and only if either ( a ) A is invertible , ( b ) 0 is an isolated point of o ( A ) , or ( c ) σ ( A ) is non - negative ( or non - positive ) . It is ...
Page 2284
... 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 = -1 L2 ( P , B , μ1 ) into [ î = 1 L1 ( P , B , μ1 ) . As the measures μ ...
... 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 = -1 L2 ( P , B , μ1 ) into [ î = 1 L1 ( P , B , μ1 ) . As the measures μ ...
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