Linear Operators, Part 2 |
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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 1993
... additive set function A is the same as the integral of the numerical function X with respect to the countably additive vector valued measure e ( o ) p . To summarize , we have the following . 4 THEOREM . Every bounded additive complex ...
... additive set function A is the same as the integral of the numerical function X with respect to the countably additive vector valued measure e ( o ) p . To summarize , we have the following . 4 THEOREM . Every bounded additive complex ...
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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero