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...

In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎w...

Employing the fact that the geometry of the N -qubit (N ≥ 2) Pauli group is embodied in the structure of the symplectic polar space W(2N − 1, 2) and using properties of the Lagrangian Grassmannian LGr(N, 2N) defined over the smallest Galois field, it is demonstrated that there exists a bijection between the set of maximum sets of mutually commuting elements of the N -qubit Pauli group and a cer...

It is surmised that the algebra of the Pauli operators on the Hilbert space of N -qubits is embodied in the geometry of the symplectic polar space of rank N and order two, W2N−1(2). The operators (discarding the identity) answer to the points of W2N−1(2), their partitionings into maximally commuting subsets correspond to spreads of the space, a maximally commuting subset has its representative ...

The well-known von Neumann inequality for commuting row contractions can be interpreted as saying that the tuple (Mz1 , . . . ,Mzn) on the Drury-Arveson space H 2 n dominates every other commuting row contraction (A1, . . . , An). We show that a similar domination relation exists among certain pairs of “lessor” row contractions (B1, . . . , Bn) and (A1, . . . , An). This hints at a possible hie...

We examine Killing spinor equations of the general IIB pp-wave backgrounds, which contain a scalar H(xm, x) in the metric and a self-dual four-form ξ(xm, x) in the self-dual five-form flux. We find that if the backgrounds admit at least one extra Killing spinor characterized by mutually commuting projection operators in addition to 16 standard Killing spinors, backgrounds must reduce to the for...

We introduce and solve a family of discrete models of 2D Lorentzian gravity with higher curvature weight, which possess mutually commuting transfer matrices, and whose spectral parameter interpolates between flat and curved space-times. We further establish a one-toone correspondence between Lorentzian triangulations and directed Random Walks. This gives a simple explanation why the Lorentzian ...