We introduce new entanglement measures on the set of density operators on
tensor product Hilbert spaces. These measures are based on the greatest cross
norm on the tensor product of the sets of trace class operators on Hilbert
space. We show that they satisfy the basic requirements on entanglement
measures discussed in the literature, including convexity, invariance under
local unitary operations and non-increase under local quantum operations and
classical communication.Comment: Revised version accepted by J Math Phys, 12 pages, LaTeX, contains
Sections 1-5 & 7 of the previous version. The previous Section 6 is now in
quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/010501