Linear Operators, Part 2 |
From inside the book
Results 1-3 of 90
Page 1965
... algebra C ( S ) of all bounded continuous complex functions on S as a B - subalgebra of eB ( S , E ) , for if e ( 8 ) ... algebra  . In case  is such an algebra of continuous functions , we shall sometimes write C instead of 2 for the ...
... algebra C ( S ) of all bounded continuous complex functions on S as a B - subalgebra of eB ( S , E ) , for if e ( 8 ) ... algebra  . In case  is such an algebra of continuous functions , we shall sometimes write C instead of 2 for the ...
Page 2194
... algebra of all operators of the form ƒ ƒ ( \ ) E ( dλ ) where ƒ is E - essentially bounded on σ ( S ) . It follows from Theorem 10 that 2 , is a full algebra of scalar type spectral operators which is equivalent to EB ( A , Σ ) . It ...
... algebra of all operators of the form ƒ ƒ ( \ ) E ( dλ ) where ƒ is E - essentially bounded on σ ( S ) . It follows from Theorem 10 that 2 , is a full algebra of scalar type spectral operators which is equivalent to EB ( A , Σ ) . It ...
Page 2214
... algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant every closed linear ...
... algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant every closed linear ...
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