What is the pilots and airliners duty in regards to carry on baggage?

Federal aviation regulations part 91, which govern general operating and flight rules, prohibit a pilot of an airplane that can seat more than 19 passengers to allow baggage aboard unless one of the following conditions are met:

• It is placed in an appropriate cargo or baggage storage compartment or
• placed under a passenger seat in such a manner that it will not "slide forward undr crash impacts severe enough to induce" inertia. 

Specifically, section 91.525 of aviation regulations part 91 disallows cargo aboard unless it is:

• properly secured by some form of tiedown, such as a safety belt,
• fastened by methods approved by the Adminitrator,
• stored in an approved cargo compartment of the airplane,
• covered or packaged in such a way to prevent potential injury to passengers,
• does not block access to  the aisle or to regular or emergency exits, and
• does not exceed the load restrictions for the floor structure and seats.