# null sequence

## null sequence

[′nəl ′sē·kwəns]
(mathematics)
A sequence of numbers or functions which converges to the number zero or the zero function.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
Mentioned in ?
References in periodicals archive ?
Following Aliprantis and Burkinshaw we say that an operator T : X [right arrow] Y is called a Dunford-Pettis operator if for each weakly null sequence ([x.sub.n]), we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
In other words ([[absolute value of [x.sub.k]/[[pi].sub.k]].sup.1/k]) is a null sequence. [[GAMMA].sub.[pi]] is called the space of entire rate sequences.
Further, let ([[member of].sub.n]) be a strictly monotonic null sequence.
A quasi-convex null sequence satisfies the class S if we take
In other words {M([[|[x.sub.k]|.sup.1/k]/[rho]])} is a null sequence. [[GAMMA].sub.M] is Called the Orlicz space of entire sequences.
Consequently, there exists a null sequence [([x.sub.n]).sub.n] in E \ { 0 } .
A sequence {[a.sub.n]} is said to be null sequence if
T [member of] V(X,Y), if T takes weakly null sequences in X to null sequences in Y.
We shall write [phi], [l.sub.[infinity]], c and [c.sub.0] for the spaces of all finite, bounded, convergent and null sequences, respectively.
Let w be the set of all sequences of real or complex numbers and let [l.sub.[infinity]], c, and [c.sub.0] be, respectively, the Banach spaces of bounded, convergent, and null sequences x = ([x.sub.k]) with the usual norm [parallel]x[parallel] = sup [absolute value of [x.sub.k]], where k [member of] N = {1,2, ...}, the set of positive integers.
Let w be the set of all sequences of real or complex numbers and [l.sub.[infinity]] c and [c.sub.0] be the linear spaces of bounded, convergent and null sequences x = ([x.sub.k]) with complex terms, respectively, normed by [[parallel]x[parallel].sup.[infinity]] = [sup.sub.k] |xk| where k [member of] N, the set of positive integers.

Site: Follow: Share:
Open / Close