Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics

Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory

The twist-deformation of the Poincaré algebra as symmetry of the field theories on noncommutative space-time with Heisenberg-like commutation relation is discussed in connection to the relation between a sound approach to the twist and the quantization in noncommutative field theory. The recent claims of violation of Pauli’s spin-statistics relation and the absence of UV/IR mixing in such theor...

Decomposition of Lebesgue Spaces

Noncommutative Spectral Decomposition with Quasideterminant

We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative CayleyHamilton’s theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it h...

Generalized Lebesgue Spaces and Application to Statistics

Statistics requires consideration of the “ideal estimates” defined through the posterior mean of fractional powers of finite measures. In this paper we study L1= , the linear space spanned by th power of finite measures, 2 (0; 1). It is shown that L1= generalizes the Lebesgue function space L1= ( ), and shares most of its important properties: It is a uniformly convex (hence reflexive) Banach s...

New Jensen and Ostrowski Type Inequalities for General Lebesgue Integral with Applications

Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.