Linear Operators: Spectral operators |
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Page 1930
... additive . However , in Corollary X.2.4 we have seen that a bounded normal operator in Hilbert space always has a uniquely defined bounded and countably additive . resolution of the identity defined on the field of all Borel subsets of ...
... additive . However , in Corollary X.2.4 we have seen that a bounded normal operator in Hilbert space always has a uniquely defined bounded and countably additive . resolution of the identity defined on the field of all Borel subsets of ...
Page 1931
... additive spectral measure E is a o - field , then E is countably additive in the strong operator topology and bounded . The boundedness of E ( o ) follows from Corollaries IV.10.2 and II.3.21 . The spectral operators in the complex B ...
... additive spectral measure E is a o - field , then E is countably additive in the strong operator topology and bounded . The boundedness of E ( o ) follows from Corollaries IV.10.2 and II.3.21 . The spectral operators in the complex B ...
Page 2144
... additive in the X topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) A ( od ) . = It is seen , by using the above remarks , that for a fixed o the family of 8 for which the equation is valid is a o - field ...
... additive in the X topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) A ( od ) . = It is seen , by using the above remarks , that for a fixed o the family of 8 for which the equation is valid is a o - field ...
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