Meaning of isotone

[prydso]

Hallo out there.


I looks to me, that this is an awesome forum I have just created my account.


Can anybody explain to me what it means when a letter is isotone? "Lemma 4.1 indicates that the operator T is isotone." I do not understand the word, and i have not any clue of what it means. I have tried to google it, but it only shows a lot of link in relation to biology and such.

Thanks in advance for your reply !!


Regards prydso

 

[HallsofIvy]

I had to look that up! According to http://www.encyclopediaofmath.org/index.php/Bounded_operator, an isotone operator (not "letter") is an operator such that if \(\displaystyle x\le y\) implies \(\displaystyle Ax\le Ay\). In other words, it does not change the order of elements. It seems to me that "Order preserving" would also work instead of "isotone".