Linear Operators: Spectral operators |
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Page 1931
... extension , ƒ ( § ) = R ( § ; T ) x , έe D ( f ) . ξερ ( Τ ) . The notion of " analytic extension " differs from that of " analytic con- tinuation , " for the domain D ( f ) of an extension may contain points which cannot be connected ...
... extension , ƒ ( § ) = R ( § ; T ) x , έe D ( f ) . ξερ ( Τ ) . The notion of " analytic extension " differs from that of " analytic con- tinuation , " for the domain D ( f ) of an extension may contain points which cannot be connected ...
Page 2092
... extension property . The example of an operator which does not have the single valued extension property that is given in Section 2 is due to S. Kakutani ( see Dunford [ 18 ] ) . Kesel'man [ 1 ] gave necessary conditions for an operator ...
... extension property . The example of an operator which does not have the single valued extension property that is given in Section 2 is due to S. Kakutani ( see Dunford [ 18 ] ) . Kesel'man [ 1 ] gave necessary conditions for an operator ...
Page 2095
... extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed , Dowson [ 3 ] notes that the unitary shift operator has quotients which do not have the single valued extension ...
... extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed , Dowson [ 3 ] notes that the unitary shift operator has quotients which do not have the single valued extension ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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