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 1960
... elements of HP are , by definition , the finite ordered sets x = [ x1 , x ] of p elements in H , and addition , scalar multiplication , and scalar products are defined in H❞ in terms of the corresponding operations in 5 by the ...
... elements of HP are , by definition , the finite ordered sets x = [ x1 , x ] of p elements in H , and addition , scalar multiplication , and scalar products are defined in H❞ in terms of the corresponding operations in 5 by the ...
Page 1966
... elements of the algebra  ' are equivalence classes where two matrices  and B are equivalent if  ( s ) = ( s ) B for e - almost all 8 in S. P For a given matrix  = ( â ,, ) in Â3 we shall use the symbol s ̧ ( 8 ) e ( ds ) for the ...
... elements of the algebra  ' are equivalence classes where two matrices  and B are equivalent if  ( s ) = ( s ) B for e - almost all 8 in S. P For a given matrix  = ( â ,, ) in Â3 we shall use the symbol s ̧ ( 8 ) e ( ds ) for the ...
Page 2265
... elements in B , n running over the cardinals ≤m ( I ) , such that ( i ) I = \\ / En · ( ii ) If En # 0 , E , has ... elements of B each having uniform multi- plicity . For each cardinal n let E , be the supremum of those Fe & with m ( F ) ...
... elements in B , n running over the cardinals ≤m ( I ) , such that ( i ) I = \\ / En · ( ii ) If En # 0 , E , has ... elements of B each having uniform multi- plicity . For each cardinal n let E , be the supremum of those Fe & with m ( F ) ...
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