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 1962
... isometric isomorphism between the B - algebras B ( H3 ) and M , ( B ( H ) ) . It should be noted that convergence in the topology defined by ( 8 ) is equivalent to convergence defined by the norm | ( a1 , ) | o = supa ,, . 1st.jsp To ...
... isometric isomorphism between the B - algebras B ( H3 ) and M , ( B ( H ) ) . It should be noted that convergence in the topology defined by ( 8 ) is equivalent to convergence defined by the norm | ( a1 , ) | o = supa ,, . 1st.jsp To ...
Page 1963
... isometric isomorphism between the spaces ( H3 ) * , and ( H * ) " and we may , when it appears that no confusion should arise , write H * = ( H * ) ” = ( H ” ) * and ** = [ x * , . . . , x * ] . p · p P. Let A be a bounded linear ...
... isometric isomorphism between the spaces ( H3 ) * , and ( H * ) " and we may , when it appears that no confusion should arise , write H * = ( H * ) ” = ( H ” ) * and ** = [ x * , . . . , x * ] . p · p P. Let A be a bounded linear ...
Page 1966
... isometric * -isomor- phism between the two algebras Ao and Âo . Since the algebras Ao and Â3 are non - commutative ( if p > 1 ) , we now give two elementary lemmas concerning B * -algebras which are not necessarily commutative . The ...
... isometric * -isomor- phism between the two algebras Ao and Âo . Since the algebras Ao and Â3 are non - commutative ( if p > 1 ) , we now give two elementary lemmas concerning B * -algebras which are not necessarily commutative . The ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
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