Zero-two law
From Encyclopedia of Mathematics
A term used for a group of results dealing with the sequence 
, where 
is a positive contraction. Usually, either this sequence converges to zero (uniformly or strongly), or for all 
the value two is associated with it. An example is the following result (see [a1] and [a2]). Let 
be a positive contraction on 
, where 
. Then either 
for all 
or 
as 
. For generalizations and additional references see [a3].
References
| [a1] | R. Zaharopol, "The modulus of a regular linear operator and the "zero-two" law in  -spaces ( ,  )" J. Funct. Anal. , 68 (1986) pp. 300–312 |
| [a2] | Y. Katznelson, L. Tzafriri, "On power bounded operators" J. Funct. Anal. , 68 (1986) pp. 313–328 |
| [a3] | A.R. Schep, "A remark on the uniform zero-two law for positive contractions" Arch. Math. , 53 (1989) pp. 493–496 |
How to Cite This Entry:
Zero-two law. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Zero-two_law&oldid=15804
Zero-two law. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Zero-two_law&oldid=15804
This article was adapted from an original article by A.R. Schep (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article