BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol.8, no.2, pp.1-15, 2014 (SCI-Expanded)
Let T be a bounded, linear operator on a complex, separable, infinite dimensional Hilbert space H. We assume that T is an essentially isometric (resp. normal) operator, that is, I-H - T*T (resp. TT* - T*T) is compact. For the compactness of S from the commutant of T, some necessary and sufficient conditions are found on S. Some related problems are also discussed.