Objective In the last few years the non-commutative moment inequalities have received a considerable attention in matrix analysis and operator theory. This phenomenon originates on the one hand in studies on the extreme properties of the standard deviation in quantum information theory, and on the other hand, in the recent concept and developments of quantum metric spaces. This research project will investigate trace inequalities in matrix algebras. Particular attention will be paid on moment inequalities for matrices with a special emphasis on their counterparts in operator algebras. It will focus on determining the best upper and lower bounds for higher order central moments in matrix algebras. This will be followed by a study of the relatively new concept of Leibniz seminorms in Banach algebras. The project will pursue a research on the strong Leibniz property of central moments in non-commutative probability spaces as well as in the classical ones in order to solve the recent question whether every centered moment has the strong Leibniz property or not. Fields of science natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesphysical sciencesquantum physicsnatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebranatural sciencesmathematicsapplied mathematicsstatistics and probabilitynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Topic(s) MSCA-IF-2014-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Call for proposal H2020-MSCA-IF-2014 See other projects for this call Funding Scheme MSCA-IF-EF-ST - Standard EF Coordinator ROYAL HOLLOWAY AND BEDFORD NEW COLLEGE Net EU contribution € 183 454,80 Address EGHAM HILL UNIVERSITY OF LONDON TW20 0EX Egham United Kingdom See on map Region South East (England) Surrey, East and West Sussex West Surrey Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 183 454,80