[1] He was married twice—to Mary Bernarda Barry and Patricia Ramsay James.
Patricia Ramsay James was a mathematician who moved into computer science as the field opened up; their one child is Kristen James Eberlein, the chair of the OASIS Darwin Information Typing Architecture Technical Committee.
[2] His doctoral students include William F. Donoghue, Jr.[3] and A. Wayne Wymore.
Eberlein also worked on spacetime models, internal symmetries in gauge theory, and spinors.
[2] His name is attached to the Eberlein–Šmulian theorem in functional analysis[4] and the Eberlein compacta in topology.