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 1957
... essential . The following elementary example shows that there are spectral operators with residual spectrum . Consider the operator Tf = g , defined in C ( [ 0 , 1 ] ) by the equation = g ( t ) = [ ' f ( x ) ... SPECTRUM OF A SPECTRAL OPERATOR.
... essential . The following elementary example shows that there are spectral operators with residual spectrum . Consider the operator Tf = g , defined in C ( [ 0 , 1 ] ) by the equation = g ( t ) = [ ' f ( x ) ... SPECTRUM OF A SPECTRAL OPERATOR.
Page 2258
... spectral theory in Chapter XX . - -- .... → 34 THEOREM . Let the closed unbounded operator S in the reflexive space X ... spectrum { λ1 , ... , λn } lends no essential com- plication to the situation at hand , so that , without loss of ...
... spectral theory in Chapter XX . - -- .... → 34 THEOREM . Let the closed unbounded operator S in the reflexive space X ... spectrum { λ1 , ... , λn } lends no essential com- plication to the situation at hand , so that , without loss of ...
Page 2515
... essential spectrum of a class of ordinary differential operators . Pacific J. Math . 14 , 755–776 ( 1964 ) . Barry ... Spectral localization of operators in Banach spaces . Math . Ann . 153 , 261-269 ( 1964 ) . 7. Spectral decomposition ...
... essential spectrum of a class of ordinary differential operators . Pacific J. Math . 14 , 755–776 ( 1964 ) . Barry ... Spectral localization of operators in Banach spaces . Math . Ann . 153 , 261-269 ( 1964 ) . 7. Spectral decomposition ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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