Linear Operators: Spectral operators |
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Page 2094
... spectral , then T * has a unique resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where *** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is ...
... spectral , then T * has a unique resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where *** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is ...
Page 2227
... spectral theory of Hermitian operators to ordinary and partial differential operators it is first necessary to extend the spectral theory of bounded operators to a theory of unbounded operators . The present chapter is an attempt to ...
... spectral theory of Hermitian operators to ordinary and partial differential operators it is first necessary to extend the spectral theory of bounded operators to a theory of unbounded operators . The present chapter is an attempt to ...
Page 2249
... spectral mapping theorem for bounded operators ( Theorem VII.3.11 ) and by Theorem 9 ( ii ) , Theorem 9 ( i ) , and Corollary 20 , it is seen that 0 € σ ( f ( TE ( e ) ... spectral resolution of T. XVIII.2.22 2249 UNBOUNDED SPECTRAL OPERATORS.
... spectral mapping theorem for bounded operators ( Theorem VII.3.11 ) and by Theorem 9 ( ii ) , Theorem 9 ( i ) , and Corollary 20 , it is seen that 0 € σ ( f ( TE ( e ) ... spectral resolution of T. XVIII.2.22 2249 UNBOUNDED SPECTRAL OPERATORS.
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