Linear Operators: Spectral operators |
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Page 2132
... index theory . In recent years the notion of the index of an operator has played a significant role in diverse areas of ... deficiency of T ) be the dimension of X / R ( T ) if this space is finite dimensional and + ∞o otherwise . An ...
... index theory . In recent years the notion of the index of an operator has played a significant role in diverse areas of ... deficiency of T ) be the dimension of X / R ( T ) if this space is finite dimensional and + ∞o otherwise . An ...
Page 2307
... deficiency indices of both be equal to an integer m . Let A , i = 1 , ... , m , be a set of m linearly independent boundary values for 7. Let S be the unbounded operator in L2 ( I ) derived from 7 by imposition of the boundary ...
... deficiency indices of both be equal to an integer m . Let A , i = 1 , ... , m , be a set of m linearly independent boundary values for 7. Let S be the unbounded operator in L2 ( I ) derived from 7 by imposition of the boundary ...
Page 2463
... deficiency indices of HV are both zero . Therefore , by Corollary XII.4.13 ( b ) , H + V is self adjoint , proving assertion ( a ) of our lemma . Q.E.D. 14 LEMMA . Let H be a self adjoint operator in H , with domain D ( H ) . Let V and ...
... deficiency indices of HV are both zero . Therefore , by Corollary XII.4.13 ( b ) , H + V is self adjoint , proving assertion ( a ) of our lemma . Q.E.D. 14 LEMMA . Let H be a self adjoint operator in H , with domain D ( H ) . Let V and ...
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