Linear Operators, Part 2 |
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Page 1941
... called the scalar part of T , and N is called the quasi- nilpotent part or the radical part of T. 5. An Operational Calculus for Bounded Spectral Operators It should be recalled that ( cf. VII.3.8-10 ) for an arbitrary bounded operator ...
... called the scalar part of T , and N is called the quasi- nilpotent part or the radical part of T. 5. An Operational Calculus for Bounded Spectral Operators It should be recalled that ( cf. VII.3.8-10 ) for an arbitrary bounded operator ...
Page 2120
... called an A - spectral function if ( i ) the map f → U , is an alge braic homomorphism with U , I , and ( ii ) the map → U12 of N into = έ Q B ( X ) is analytic on the complement of the support of f . An operator SE B ( X ) is called ...
... called an A - spectral function if ( i ) the map f → U , is an alge braic homomorphism with U , I , and ( ii ) the map → U12 of N into = έ Q B ( X ) is analytic on the complement of the support of f . An operator SE B ( X ) is called ...
Page 2132
... ( called the deficiency of T ) be the dimension of X / R ( T ) if this space is finite dimensional and + ∞o otherwise . An operator T will be called a Fredholm operator in case R ( T ) is closed and both x ( T ) and ẞ ( T ) are finite ...
... ( called the deficiency of T ) be the dimension of X / R ( T ) if this space is finite dimensional and + ∞o otherwise . An operator T will be called a Fredholm operator in case R ( T ) is closed and both x ( T ) and ẞ ( T ) are finite ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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