Yes, it can do it. But itβs good to stick to the recommended icon sizes. Since working with user interface recommendations goes a long way.
To make your left icon inactive, try setHomeButtonEnabled . Since this api is only available on ICS and above, and in previous versions, the icon is enabled by default. Thus, you can have an active icon that does nothing. (Well, you can live with this restriction, since there are not many 3.x devices there)
A custom view is your view, so its desire to make it clickable or not. To add a custom view,
mActionBar = getActionBar(); mActionBar.setDisplayShowTitleEnabled(false);
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