topologically nilpotent

An element a in a normed ringMathworldPlanetmath A is said to be topologically nilpotent if


Topologically nilpotent elements are also called quasinilpotent.


  • Any nilpotent elementMathworldPlanetmath is topologically nilpotent.

  • If a and b are topologically nilpotent and ab=ba, then ab is topologically nilpotent.

  • When A is a unital Banach algebraMathworldPlanetmath, an element aA is topologically nilpotent iff its spectrum σ(a) equals {0}.

Title topologically nilpotent
Canonical name TopologicallyNilpotent
Date of creation 2013-03-22 16:12:04
Last modified on 2013-03-22 16:12:04
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 6
Author CWoo (3771)
Entry type Definition
Classification msc 46H05
Synonym quasinilpotent