Linear Operators: Spectral operators |
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Page 2112
... sets , and G1 and G2 are open 1 sets which cover C. ( It should be noted that T and T * play symmetric roles in ( i ) and ( iv ) . ) An example is given to show that not every operator admits a duality theory of type 1 ; however , if T ...
... sets , and G1 and G2 are open 1 sets which cover C. ( It should be noted that T and T * play symmetric roles in ( i ) and ( iv ) . ) An example is given to show that not every operator admits a duality theory of type 1 ; however , if T ...
Page 2203
Nelson Dunford, Jacob T. Schwartz. contains every open set . Let e be an open subset of 4 , let x and x * be elements of X , X * , respectively , and let ɛ > 0 . Then , because of the regularity of xA ( ) x * , there is a closed subset 8 ...
Nelson Dunford, Jacob T. Schwartz. contains every open set . Let e be an open subset of 4 , let x and x * be elements of X , X * , respectively , and let ɛ > 0 . Then , because of the regularity of xA ( ) x * , there is a closed subset 8 ...
Page 2233
... open set U such that E ( U ) I. Let { e } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( U - 1 en ) = I. The operator f ( T ) is defined by the equations n D ( ƒ ( T ' ) ) = { x ...
... open set U such that E ( U ) I. Let { e } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( U - 1 en ) = I. The operator f ( T ) is defined by the equations n D ( ƒ ( T ' ) ) = { x ...
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