About: Topological divisor of zero

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In mathematics, an element of a Banach algebra is called a topological divisor of zero if there exists a sequence of elements of such that 1. * The sequence converges to the zero element, but 2. * The sequence does not converge to the zero element. If such a sequence exists, then one may assume that for all . If is not commutative, then is called a "left" topological divisor of zero, and one may define "right" topological divisors of zero similarly.

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  • Ein topologischer Nullteiler ist ein Begriff aus der mathematischen Theorie der Banachalgebren. Unter Ausnutzung der Topologie wird der algebraische Begriff des Nullteilers verallgemeinert. (de)
  • In mathematics, an element of a Banach algebra is called a topological divisor of zero if there exists a sequence of elements of such that 1. * The sequence converges to the zero element, but 2. * The sequence does not converge to the zero element. If such a sequence exists, then one may assume that for all . If is not commutative, then is called a "left" topological divisor of zero, and one may define "right" topological divisors of zero similarly. (en)
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  • Ein topologischer Nullteiler ist ein Begriff aus der mathematischen Theorie der Banachalgebren. Unter Ausnutzung der Topologie wird der algebraische Begriff des Nullteilers verallgemeinert. (de)
  • In mathematics, an element of a Banach algebra is called a topological divisor of zero if there exists a sequence of elements of such that 1. * The sequence converges to the zero element, but 2. * The sequence does not converge to the zero element. If such a sequence exists, then one may assume that for all . If is not commutative, then is called a "left" topological divisor of zero, and one may define "right" topological divisors of zero similarly. (en)
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  • Topologischer Nullteiler (de)
  • Topological divisor of zero (en)
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