Linear Operators: Spectral operators |
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Page 1912
... theorem , which is used only in the proof of a corollary unessential to the main train of ideas . The reader of ... spectral theorem for bounded self adjoint operators . This spectral theorem for self adjoint operators is not logically ...
... theorem , which is used only in the proof of a corollary unessential to the main train of ideas . The reader of ... spectral theorem for bounded self adjoint operators . This spectral theorem for self adjoint operators is not logically ...
Page 1965
... spectral measure e ( · ) , whose existence is asserted by the spectral theorem , has the property just mentioned ; that is , e ( o ) 0 if o is non - void and open . To see this we note that , since is a normal space ( 1.5.9 ) , Urysohn's ...
... spectral measure e ( · ) , whose existence is asserted by the spectral theorem , has the property just mentioned ; that is , e ( o ) 0 if o is non - void and open . To see this we note that , since is a normal space ( 1.5.9 ) , Urysohn's ...
Page 2516
Nelson Dunford, Jacob T. Schwartz. 2 . The spectral mapping theorem for a Hermitian operator . Amer . Math . Monthly 70 , 1049-1051 ( 1963 ) . 3. A note on operators whose spectrum is a spectral set . Acta Sci . Math . Szeged 27 , 201 ...
Nelson Dunford, Jacob T. Schwartz. 2 . The spectral mapping theorem for a Hermitian operator . Amer . Math . Monthly 70 , 1049-1051 ( 1963 ) . 3. A note on operators whose spectrum is a spectral set . Acta Sci . Math . Szeged 27 , 201 ...
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