Linear Operators, Part 2 |
From inside the book
Results 1-3 of 43
Page 1926
... normal operator , then ( T — XI ) E ( X ) = 0 and this formula reduces to the formula ƒ ( T ) = Σ ƒ ( \ ) E ( X ) , λεσ ( Τ ) which is not valid for an arbitrary T. To see more clearly the difference between the calculi given by these ...
... normal operator , then ( T — XI ) E ( X ) = 0 and this formula reduces to the formula ƒ ( T ) = Σ ƒ ( \ ) E ( X ) , λεσ ( Τ ) which is not valid for an arbitrary T. To see more clearly the difference between the calculi given by these ...
Page 1978
... operators , we observe that a self adjoint operator or , more generally , a normal operator in A is a spectral operator . For if A is a normal operator in A " , it follows from Theorem 9.3 that for e - almost all s in the p × p matrix  ( s ) ...
... operators , we observe that a self adjoint operator or , more generally , a normal operator in A is a spectral operator . For if A is a normal operator in A " , it follows from Theorem 9.3 that for e - almost all s in the p × p matrix  ( s ) ...
Page 2005
... operator A in 2 , not of the form A = AI with λ in A , has a non - zero radical part if e ( S1 ) 0. By Theo- rem 6.4 the spectral operators with non - zero radical parts are the only ones not similar to normal operators . Thus both of ...
... operator A in 2 , not of the form A = AI with λ in A , has a non - zero radical part if e ( S1 ) 0. By Theo- rem 6.4 the spectral operators with non - zero radical parts are the only ones not similar to normal operators . Thus both of ...
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