Glasnik Matematicki, Vol. 45, No.2 (2010), 505-512.

CONTINUITY OF THE POLAR DECOMPOSITION FOR UNBOUNDED OPERATORS ON HILBERT C*-MODULES

Kamran Sharifi

Department of Mathematics, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran
e-mail: sharifi.kamran@gmail.com & sharifi@shahroodut.ac.ir


Abstract.   For unbounded operators t,s between Hilbert C*-modules which admit the polar decompositions V|t|, W|s|, respectively, we obtain an explicit upper bound estimate for the gap between t and s in terms of the norm of the bounded operators V-W, C|t|-C|s| and C|t*|-C|s*|, where C|t| and C|s| are the Cayley transforms of |t| and |s|. The result are used to drive a criterion for continuity of the polar decomposition for unbounded operators between Hilbert C*-modules.

2000 Mathematics Subject Classification.   46L08, 46C50, 47C15, 47B50.

Key words and phrases.   Hilbert C*-module, unbounded operator, gap metric, Cayley transform.


Full text (PDF) (free access)

DOI: 10.3336/gm.45.2.15


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