Linear Operators, Part 2 |
From inside the book
Results 1-3 of 78
Page 1945
... Operators in Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space H and the bounded normal operators in $ ? The central result in this direction is a theorem of Wermer which states that every ...
... Operators in Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space H and the bounded normal operators in $ ? The central result in this direction is a theorem of Wermer which states that every ...
Page 1947
... Hilbert space $ . Then there exists a bounded self adjoint operator B in 5 with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection ... OPERATORS IN HILBERT SPACE Bounded Spectral Operators in Hilbert Space.
... Hilbert space $ . Then there exists a bounded self adjoint operator B in 5 with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection ... OPERATORS IN HILBERT SPACE Bounded Spectral Operators in Hilbert Space.
Page 2169
... operator . Q.E.D. 6. Self Adjoint Operators in Hilbert Space It is the purpose of this section to show how the theory of spectral operators may be applied to yield the classical spectral theorem in Hilbert space , that is , the theorem ...
... operator . Q.E.D. 6. Self Adjoint Operators in Hilbert Space It is the purpose of this section to show how the theory of spectral operators may be applied to yield the classical spectral theorem in Hilbert space , that is , the theorem ...
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