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.
We study dilations of q-commuting tuples. Bhat, Bhattacharyya and Dey gave the correspondence between the two standard dilations of commuting tuples and here these results are extended to q-commuting tuples. We are able to do this when the q-coefficients are of modulus one. We introduce a “maximal q-commuting subspace” of an n-tuple of operators and a “standard q-commuting dilation”. Our main result is that the maximal q-commuting subspace of the standard noncommuting dilation of a q-commuting...
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