Linear Operators: Spectral operators |
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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 A - scalar if there exists an A - spectral function U : A → B ( X ) such that SU11 ( where f1 ( A ) = λ ) . Every scalar type spectral operator is A - scalar , with the algebra of bounded Borel functions . Similarly , if X = L ...
... called A - scalar if there exists an A - spectral function U : A → B ( X ) such that SU11 ( where f1 ( A ) = λ ) . Every scalar type spectral operator is A - scalar , with the algebra of bounded Borel functions . Similarly , if X = L ...
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 a ( 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 a ( T ) and ẞ ( T ) are finite ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero