Standard commuting dilations and liftings

Volume 126 / 2012

Santanu Dey Colloquium Mathematicum 126 (2012), 87-94 MSC: Primary 47A20; Secondary 47A13, 47A15, 46L05. DOI: 10.4064/cm126-1-5

Abstract

We identify how the standard commuting dilation of the maximal commuting piece of any row contraction, especially on a finite-dimensional Hilbert space, is associated to the minimal isometric dilation of the row contraction. Using the concept of standard commuting dilation it is also shown that if liftings of row contractions are on finite-dimensional Hilbert spaces, then there are strong restrictions on properties of the liftings.

Authors

  • Santanu DeyDepartment of Mathematics
    Indian Institute of Technology Bombay
    Powai, Mumbai 400076, India
    e-mail

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