Linear Operators: Spectral operators |
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Page 2011
... defined almost everywhere on but not necessarily bounded . For every set σ in Σ and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined operator ...
... defined almost everywhere on but not necessarily bounded . For every set σ in Σ and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined operator ...
Page 2018
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( Ag ) -1 exists as a bounded everywhere defined operator . The spectrum σ ( A ) of A is defined to be the complement p ( A ̧ ) . It is clear from the equation ...
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( Ag ) -1 exists as a bounded everywhere defined operator . The spectrum σ ( A ) of A is defined to be the complement p ( A ̧ ) . It is clear from the equation ...
Page 2284
... defined on the Borel sets of the plane P are positive and vanish outside e ,. Moreover , there is a natural continuous linear map T1 of E , into [ î - 1 L1 ( P , B , μ1 ) with densely defined inverse . Let W2 denote the identity map of ...
... defined on the Borel sets of the plane P are positive and vanish outside e ,. Moreover , there is a natural continuous linear map T1 of E , into [ î - 1 L1 ( P , B , μ1 ) with densely defined inverse . Let W2 denote the identity map of ...
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