Can L1 B visa holder run a business?

Can L1 B visa holder run a business? or more specifically, if he wants to launch his own website and try to earn through it (advertisements etc., it is a sort of business, right?), is that legal? Also, which official organisation (USCIS, I guess.) to contact to confirm?

[Lexus]

It seems that starting a business while in the United States on an L-1B visa (or any type of visa) is generally an easy process, depending on the state in which you reside. You will get a number of benefits for your business such as Tax benefits, liability protections etc. But there are some strict requirements concerning work authorization while you are on a L1B visa.

Determine the proper corporate entity. Under U.S. law, there exist several different types of corporate structures such as C-corporations, S-corporations, partnerships, limited liability companies, limited partnerships and others. Secondly Incorporation comes; you have to register your business that can be done through on line. You have to get Tax Identification Number, Open corporate bank accounts. You contact with USCIS they will provide you the formalities to be complied with .It is also advised that you consult an Account and an Attorney for protecting yourself and your business form Tax liabilities and Legal liabilities.

Can you please explain further, " But there are some strict requirements concerning work authorization while you are on a L1B visa."