Linear Operators: Spectral operators |
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Page 2095
... scalar type operators also hold for their quotients . D Although the restrictions of operators with the single valued extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true ...
... scalar type operators also hold for their quotients . D Although the restrictions of operators with the single valued extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true ...
Page 2106
... scalar type operator of class ( X ) , and ( ii ) if X is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and X is weakly complete , then A is scalar type if and only if either ( a ) A is ...
... scalar type operator of class ( X ) , and ( ii ) if X is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and X is weakly complete , then A is scalar type if and only if either ( a ) A is ...
Page 2174
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { e1t | t € R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { e1t | t € R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
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