Linear Operators: Spectral operators |
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Page 2265
... multiplicity function on B which is an extension of m on D. α PROOF . If E € B define m ( E ) = \ / \ / a m ( Ba ) , where { B } is any family in D such that E ... multiplicity function for B it will XVIII.3.2 2265 MULTIPLICITY THEORY.
... multiplicity function on B which is an extension of m on D. α PROOF . If E € B define m ( E ) = \ / \ / a m ( Ba ) , where { B } is any family in D such that E ... multiplicity function for B it will XVIII.3.2 2265 MULTIPLICITY THEORY.
Page 2283
... multiplicity n if and only if its adjoint E * in B * has finite uniform multiplicity n . PROOF . It is sufficient to suppose E and E * satisfy the countable chain condition . Also since each projection is the union of projections of ...
... multiplicity n if and only if its adjoint E * in B * has finite uniform multiplicity n . PROOF . It is sufficient to suppose E and E * satisfy the countable chain condition . Also since each projection is the union of projections of ...
Page 2288
... multiplicity theory as presented in Section 3 is due to W. G. Bade [ 5 ] . J. Dieudonné [ 20 ] had previously obtained a multiplicity theory in the case where the adjoint * of the underlying Banach space X is separable ( which implies ...
... multiplicity theory as presented in Section 3 is due to W. G. Bade [ 5 ] . J. Dieudonné [ 20 ] had previously obtained a multiplicity theory in the case where the adjoint * of the underlying Banach space X is separable ( which implies ...
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