Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 79
Page 2256
... zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. 1 PROOF . Suppose first that ... zero is contained in an arbitrarily small compact set open in the relative topology of o ( R ) . - 1 - Suppose now ...
... zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. 1 PROOF . Suppose first that ... zero is contained in an arbitrarily small compact set open in the relative topology of o ( R ) . - 1 - Suppose now ...
Page 2292
... zero and at most a denumerable sequence of points μn 0 tending to zero . For each of these points μn , there exists a non - zero vector x , such that T - 1xn Mn xn . It follows that Txn = μñ1xn , so that o ( T ) ≥ { μ1 } . On the other ...
... zero and at most a denumerable sequence of points μn 0 tending to zero . For each of these points μn , there exists a non - zero vector x , such that T - 1xn Mn xn . It follows that Txn = μñ1xn , so that o ( T ) ≥ { μ1 } . On the other ...
Page 2325
... zero of sin ( za ) = B. Put R ( 1 ) = R ( 1 ) + 2mπ , R ( 2 ) = R ( 2 ) + 2mπ . Taking our cue from the known form 27m + a + 21 , 2πm + a +22 , 21 # 22 , 2π > RZ1 ≥ Rz2 ≥ 0 of the zeros of sin ( z — α ) — ẞ , we wish to show that for ...
... zero of sin ( za ) = B. Put R ( 1 ) = R ( 1 ) + 2mπ , R ( 2 ) = R ( 2 ) + 2mπ . Taking our cue from the known form 27m + a + 21 , 2πm + a +22 , 21 # 22 , 2π > RZ1 ≥ Rz2 ≥ 0 of the zeros of sin ( z — α ) — ẞ , we wish to show that for ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero