• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.653-659
• /
• 1995

We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.