Linear Operators, Part 2 |
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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 = 9 ( 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 = 9 ( t ) = f ( x ) ... SPECTRUM OF A SPECTRAL OPERATOR.
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 ...
Page 2565
... essential spectrum . Bull . Amer . Math . Soc . 71 , 365-367 ( 1965 ) . 2. On the essential spectrum of an arbitrary operator I. J. Math . Anal . Appl . 13 , 205-215 ( 1966 ) . Schreiber , M. 2. Unitary dilations of operators . Duke ...
... essential spectrum . Bull . Amer . Math . Soc . 71 , 365-367 ( 1965 ) . 2. On the essential spectrum of an arbitrary operator I. J. Math . Anal . Appl . 13 , 205-215 ( 1966 ) . Schreiber , M. 2. Unitary dilations of operators . Duke ...
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