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 1971
... u . Since 0 = d ( λ1 ( T ) ; гm ) → d ( u ; To ) , it follows that either ... measurable function of I. The proof may be completed by choosing λ ( Ã ) to ... measurable map from B ( EP ) . Then there are E - measurable scalar functions 1 ...
... u . Since 0 = d ( λ1 ( T ) ; гm ) → d ( u ; To ) , it follows that either ... measurable function of I. The proof may be completed by choosing λ ( Ã ) to ... measurable map from B ( EP ) . Then there are E - measurable scalar functions 1 ...
Page 1972
... measurable . Q.E.D. 3 LEMMA . Let s → T ( s ) be a Σ - measurable map from S into B ( E ” ) . Then there are ... U { 8 | √1 ( 8 ) = ··· = √x ( 9 ) ‡ dx + 1 ( 8 ) = ··· = { p ( 8 ) } , 637 = k = 1 U { s¦√1 ( 8 ) = ··· = { x ( 8 ) ‡ Xx ...
... measurable . Q.E.D. 3 LEMMA . Let s → T ( s ) be a Σ - measurable map from S into B ( E ” ) . Then there are ... U { 8 | √1 ( 8 ) = ··· = √x ( 9 ) ‡ dx + 1 ( 8 ) = ··· = { p ( 8 ) } , 637 = k = 1 U { s¦√1 ( 8 ) = ··· = { x ( 8 ) ‡ Xx ...
Page 2096
... U ( ƒ ) of the space of bounded Borel functions measurable on Z into B ( X ) such that ( i ) I = U ( fo ) for f 。( A ) = 1 and T = U ( f1 ) for ƒ1 ( λ ) = λ , ( ii ) U ( ƒƒ1 ) = U ( ƒ ) T for all ƒ , ( iii ) if { f } is a bounded ...
... U ( ƒ ) of the space of bounded Borel functions measurable on Z into B ( X ) such that ( i ) I = U ( fo ) for f 。( A ) = 1 and T = U ( f1 ) for ƒ1 ( λ ) = λ , ( ii ) U ( ƒƒ1 ) = U ( ƒ ) T for all ƒ , ( iii ) if { f } is a bounded ...
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