Yes, Jonathan B. Turell is the son of Saul J. Turell. Here is Saul's brief bio 
from the All Movie Guide:

Saul J. Turell succeeded at enough different aspects of the movie business for 
any three careers: as a distributor and producer of documentary films, a 
pioneer in the field of cable television, a distributor of classic feature 
films from the 1920s through the 1960s, and as an Oscar-winning filmmaker. 
Turell was a key figure in facilitating the revival of interest in classic 
cinema during the 1960s, 1970s, and 1980s. 

Some time in the early 1970s, I believe, Saul Turell and William Becker 
purchased Janus Films, the famous distributor founded in the 1950s by Bryant 
Haliday and Cyrus Harvey, Jr. that was responsible for introducing American 
audiences to Fellini, Bergman, Kurosawa, and the like in the 1950s and 1960s 
and whose library now forms the foundation of The Criterion Collection. Turell 
and Becker's sons, Jonathan Turell and Peter Becker, are now CEO and president 
of the Criterion Collection, respectively.

Quoting "Steven P. Hill" <[log in to unmask]>:

> Dear colleagues:
> On 8/4/05 I posted on "SCREEN-L" the huge news release about Image
> Entertainment acquiring Home Vision and the Criterion Collection.   In
> the last half of that huge text, the chief  ("CEO") of Criterion is
> identified
> as Jonathan Turell.
> Rr-reading that text today, I happened to recall,  from four or five decades
> ago, that same name "Turell," prefaced by a given name like  "Sol" or
> "Paul."
> I think there may have been a partnership like Turell & Killiam (if memory
> serves), linked with the collecting and distribution of celluloid golden
> oldies from the silent days.  Perhaps it would have been various packages
> or series like "Silents Please" or "Hollywood and the Stars," which were
> telecast in the 1950s and/or 1960s.
> And I turn to you colleagues with a small question:  is Criterion's Jonathan
> Turell in 2005 related to that  collector and distributor of oldies, Sol (or
> Paul) Turell, a half-century ago?
> Gratefully,
> Steven P Hill,
> University of Illinois.
> ----
> Online resources for film/TV studies may be found at ScreenSite

Online resources for film/TV studies may be found at ScreenSite