Linear Operators, Part 2 |
From inside the book
Results 1-3 of 28
Page 1993
... respect to the finitely 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 ...
... respect to the finitely 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 ...
Page 2104
... respect to one consistent semi - inner product , it has a real numerical range with respect to all . Lumer called such operators Hermitian operators on X ; he further showed that this 2104 XV.16 XV . SPECTRAL OPERATORS.
... respect to one consistent semi - inner product , it has a real numerical range with respect to all . Lumer called such operators Hermitian operators on X ; he further showed that this 2104 XV.16 XV . SPECTRAL OPERATORS.
Page 2403
... respect to two - dimensional Lebesgue measure . A first application ( Theorem 6 ) is made in this way , and immediately following upon this we develop a similar but consider- ably generalized result ( Theorem 7 ) whose hypotheses accord ...
... respect to two - dimensional Lebesgue measure . A first application ( Theorem 6 ) is made in this way , and immediately following upon this we develop a similar but consider- ably generalized result ( Theorem 7 ) whose hypotheses accord ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 other sections not shown
Other editions - View all
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