Related papers: A note on commutative and noncommutative Gurariy s…
We present a short and elementary proof of isometric uniqueness of the Gurarii space.
We show that the algebra of functions on noncommutative space allows two different representations. One is describing the genuine noncommutative space, while another one can be rewritten in commutative form by a redefinition of generators.
Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.
The aim of this contribution is twofold. First, we show that when two (or more) different quantum groups share the same noncommutative spacetime, such an 'ambiguity' can be resolved by considering together their corresponding noncommutative…
In this note we show that in a two-dimensional non-commutative space the area operator is quantized, this outcome is compared with the result obtained by Loop Quantum Gravity methods.
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
Various approaches by the author and collaborators to define gravitational fluctuations associated with a noncommutative space are reviewed.
We show the dual spaces of conditional Hardy space and symmetric Hardy space of noncommutative martingales. We derive relationship between the symmetric Hardy space of noncommutative martingales and its conditioned version.
In this article, we will define non-commutative covering spaces using Hopf-Galois theory. We will look at basic properties of covering spaces that still hold for these non-commutative analogues. We will describe examples including coverings…
In this short note is on the equivalence between non-Newtonian metric (particularly multiplicative metric) and metric. We present a different proof the fact that the notion of a non-Newtonian metric space is not more general than that of a…
A review is made of recent efforts to add a gravitational field to noncommutative models of space-time. Special emphasis is placed on the case which could be considered as the noncommutative analog of a parallelizable space-time. It is…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
We present selected known results and some of their improvements, involving Gurarii spaces. A Banach space is Gurarii if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the…
This note surveys Wolfgang Lusky's proof of uniqueness of the Gurariy spaces and mentions further developments.
We first give a new proof and also a new formulation for the Abhyankar-Gurjar inversion formula for formal maps of affine spaces. We then use the reformulated Abhyankar-Gurjar formula to give a more straightforward proof for the equivalence…
In this paper we give some relationship between G-metric spaces, partial metric spaces and GP-metric spaces.
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal $\star$-product on…
The gauge connections corresponding to electromagnetism, Yang-Mills theory and Einstein gravity can be derived by assuming specific commutation relations between the phase-space variables of a first quantized theory. Extending the procedure…