Linux will continue to grow in this market, but IT managers seem wary of converting over from Solaris or HP-UX right now in some businesses. Personally I see Linux dominating the small to mid size businesses and Unix being the mainstay of the larger corporate world - one reason being single source, we have agreements with SUN to manage all the hardware and OS and if we have problems we have one company and one OS to deal with and those are highlighted by a large, organized company backing them.
My point in that is there is a 'feeling' of security when dealing with a company where the hardware and OS are backed up with years of technology and direction, whereas many I have talked to (rightly or wrongly) see Linux more as loosely affiliated group of dedicated users and developers without a big organization to back them up when in need. If the big Linux ditributors overcome this I can see it getting more of a corporate foothold (it already has some) in the high end back room server market.
Disclosure note: I work at a data center for a bank and we deal in very high end applications to serve large companies' financial needs, as well as general population banking, and the thought of converting all those apps onto Linux machines scares the heck out of people. We run several different unix OSes, though mainly Solaris now, and windows 2000 advanced/datacenter servers for a variety of web applications. While we do have a large group of main frames still in use (and probably will for many years to come) we have been migrating some of those to high end sunfire boxes (a trend that will continue).