A range-kernal orthogonality property is established for the elementary operators (X) = ∑n i=1AiXBi and ∗(X) = ∑n i=1A ∗ i XB ∗ i , where A = (A1,A2, . . . ,An) and B = (B1,B2, . . . ,Bn) are n-tuples of mutually commuting scalar operators (in the sense of Dunford) in the algebra B(H) of operators on a Hilbert space H . It is proved that the operator satisfies Weyl’s theorem in the case in whic...

Here we study dilations of q-commuting tuples. In [BBD] the authors gave the correspondence between the two standard dilations of commuting tuples and here these results have been extended to q-commuting tuples. We are able to do this when q-coefficients ‘qij ’ are of modulus one. We introduce ‘maximal q-commuting subspace ’ of a n-tuple of operators and ‘standard q-commuting dilation’. Our mai...