There are several things you can do to improve your Sony Xperia Z1s performance.
Check the following:
Available RAM and phone memory Begin by checking how much available RAM and phone storage you have. If these memories drops low the performance may be affected. We recommend that you have at least 10% free phone memory. You can check your Sony Xperia Z1 memory by going to: Settings > Storage.
You can free up some phone memory by moving supported apps to SD card or internal storage.
Disable apps This feature is available in Android 4.0 (ICS) and later versions. You can disable both third party and most preinstalled apps so they dont run in the background. You can do this by going to: Settings > Apps > All > Select your app > Disable.
Live Wallpaper Do you use any Live Wallpaper? These generally consume a lot of RAM memory making the Sony Xperia Z1 feel slow and laggy depending on available RAM of course. Try to use an ordinary wallpaper if you want to improve performance.
Widgets Having many widgets active on the home screen will also use a lot of RAM memory. So reducing the amount of widgets on home screen will speed up the UI performance.
Up time When was the last time you rebooted your Sony Xperia Z1? You can check this by going to: Settings > About phone > Status > Up time. It doesnt hurt to reboot your Sony Xperia Z1 every now and then.
Task killers We dont really recommend you using task killers if youre not sure on how to configure them. By default most task killers are set to close all applications running in the background which can cause problems with applications, widgets and also drain battery since many preinstalled applications will automatically start running again.
If you have an Xperia phone with 512MB of RAM memory and plan to update to Android 4.0 (ICS) you should be aware of that Android 4.0s hardware requirements are more advanced than previous softwares so your phones performance may be affected.