Linear Operators, Part 2 |
From inside the book
Results 1-3 of 59
Page 2116
... bounded Borel ) functions of a self adjoint operator in Hilbert space , as presented in Chapter X , have been known ... function fo ( A ) = 1 into I and the function f1 ( λ ) = λ into T. Once this point of view has been taken it is very ...
... bounded Borel ) functions of a self adjoint operator in Hilbert space , as presented in Chapter X , have been known ... function fo ( A ) = 1 into I and the function f1 ( λ ) = λ into T. Once this point of view has been taken it is very ...
Page 2169
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
Page 2188
... bounded Borel measurable function defined on the complex plane . Then √ g ( f ( x ) ) E ( dx ) = √ , 9 ( μ ) E ( ƒ − 1 ( dμ ) ) , A f ( A ) fe EB ( 1 , 2 ) . PROOF . Let f be in EB ( A , Σ ) , and for every Borel set 8 in the complex ...
... bounded Borel measurable function defined on the complex plane . Then √ g ( f ( x ) ) E ( dx ) = √ , 9 ( μ ) E ( ƒ − 1 ( dμ ) ) , A f ( A ) fe EB ( 1 , 2 ) . PROOF . Let f be in EB ( A , Σ ) , and for every Borel set 8 in the complex ...
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