in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

A master equation (n dimensional non–Abelian current conservation law with mutually commuting current components) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic way to understand 2-d integrable non-linear equations as well as 4-d self-dual equations and, more importantly, their generalizations to higher dimensions.

Let H 2 ( D n ) denote the Hardy space over polydisc , ≥ . A closed subspace Q ⊆ is called Beurling quotient module if there exists an inner function θ ∈ ∞ such that = / We present a complete characterization of modules : be subspace, and let C z i P M | 1 … Then only I − ⁎ j 0 ≠ two applications: first, we obtain dilation theorem for Brehmer -tuples commuting contractions, and, second, relate ...

A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N -qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and partitionings of the corresponding Pauli graph are embodied in the geometry of the generalized q...

Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that and transform have the same joint essential spectrum. Further, it shown spectrum contained in numerical range

An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators. Denote by L(X) the algebra of all bounded linear operators i...