- be
nilpotent if Tn = 0 for some
positive integer n. It is said to be
quasinilpotent or
topologically nilpotent if its
spectrum σ(T) = {0}. In the finite-dimensional...
- superdiagonal,
equality may be violated. The
quasinilpotent operators is one
class of such examples. A
nonzero quasinilpotent operator A {\displaystyle A} has spectrum...
- eigenvalue. A
bounded operator A : X → X {\displaystyle A:\,X\to X} is
quasinilpotent if ‖ A n ‖ 1 / n → 0 {\displaystyle \lVert A^{n}\rVert ^{1/n}\to 0}...
-
spectral theory of
compact operators, its
spectrum σ(V) = {0}. V is a
quasinilpotent operator (that is, the
spectral radius, ρ(V), is zero), but it is not...
- Foiaş, Ciprian; Jung, Il Bong; Ko, Eungil; Pearcy, Carl (2005). "On
quasinilpotent operators. III".
Journal of
Operator Theory. 54 (2): 401–414.. Enflo's...
- both a left and
right topological divisor of zero. In particular, any
quasinilpotent element is a
topological divisor of zero (e.g. the
Volterra operator)...
-
discontinuity for
derivations on
Frechet algebras Radical Banach Algebrasand Quasinilpotent Weighted Shift Operators. The
image of a
derivation is
contained in...
- }}A{\mbox{ with
finite algebraic multiplicity}}\}.} In particular, for a
quasinilpotent operator Q : l 2 ( N ) → l 2 ( N ) , Q : ( a 1 , a 2 , a 3 , … ) ↦ (...
- Foiaş, Ciprian; Jung, Il Bong; Ko, Eungil; Pearcy, Carl (2005). "On
quasinilpotent operators. III".
Journal of
Operator Theory. 54 (2): 401–414.. Enflo's...
