It’s Apple week in the tech world, what with the MacWorld conference taking center stage in San Francisco. Today, Google (whose CEO Eric Schmidt sits on the Apple board) announced an update to its online applications that optimizes them for running on Apple’s iPhone.

Google had already rolled out iPhone-specific versions of its applications – including Gmail, Google Calendar, Google Reader and other productivity apps. Today, Google focused on announcing improvements to how those applications run on the iPhone.

For instance, improvements to the user interface makes the apps “feel faster,” Google said, and are more optimized for navigation via the iPhone touch-screen. In addition, Google sped up performance of its mail and calendar applications, including “push-style” email that delivers new emails to the phone when they arrive.

Perhaps most interestingly, Google said it has now brought its iGoogle gadgets – small software programs – to the iPhone. iGoogle gadgets offer weather and stock updates, news feeds and more, which can now be viewed on the iPhone.

Apple is expected to introduce its own “gadget” strategy this week when it formally unveils a software kit for the iPhone. Last week, Yahoo unveiled an update to its Web content strategy, including an SDK for letting third-party developers add widgets to its platform.

The close relationship between Apple and Google would seem to derive at least in part from the Eric Schmidt relationship, although the two companies’ strategies dovetail nicely as well, in particular as they team to take on competitors, most notably Microsoft.