__Marie Curie IF Project 'MOMENTS':__

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 aimed to investigate trace inequalities in matrix algebras. Particular attention has been paid to moment inequalities for matrices with a special emphasis on their counterparts in operator algebras. The focus is on determining the best upper and lower bounds for higher order central moments in matrix algebras. This is followed by a study of the relatively new concept of Leibniz seminorms in Banach algebras. The project has pursued 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 or not every centred moment has the strong Leibniz property.

So far, our findings have been summarized in the following papers:

- Leka Z., Rearrangements and Leibniz-type rules of mean oscillations, to appear in J. Math. Anal. Appl.
- Leka Z., Some singular value inequalities by convexity, Linear and Multilinear Algebra,
- https://doi.org/10.1080/03081087.2017.1418829
- Leka Z., On the Leibniz rule for random variables, Math. Inequal. Appl., 21:(1) 235-249, (2018)
- Leka Z., Symmetric seminorms and the Leibniz property, J. Math. Anal. Appl., 452:(1) 708-725, (2017).
- Leka Z., Some inequalities for central moments of matrices, Lin. Alg. Appl., 496:(1) 246-261, (2016).

__Further publications:__

- Besenyei Á., Léka Z., Leibniz seminorms in probability spaces, J. Math. Anal. Appl., 429:(2) 1178-1189, (2015).
- Léka Z., On discrete time regularity of bounded linear operators, to appear in Banach Center Publ.
- Léka Z., A note on extremal decomposition of covariances, Rocky Mountain J. Math., 46:(2) 571–580 (2016).
- Léka Z., A note on central moments in C*-algebras, J. Math. Inequal., 9:(1) 165-175, (2015).
- Léka Z., Time regularity and functions of the Volterra operator, Stud. Math., 220:(1) 1-14, (2014).
- Léka Z., Petz D., Some decompositions of matrix variances, Probab. Math. Statist., 33:(2) 191-199, (2013).
- Léka Z., On orbits of functions of the Volterra operator, Comp. Anal. Oper. Theory, 7:(4) 1321-1335, (2013).
- Léka Z., A note on the powers of Cesàro bounded operators, Czechoslovak Math. J., 60:(4) 1091-1100, (2010).
- Léka Z., A Katznelson-Tzafriri type theorem in Hilbert spaces, Proc. Amer. Math. Soc., 137:(11) 3763-3768, (2009).
- Léka Z., Characterization of C0-semigroups with regular norm-function, Acta Sci. Math. (Szeged), 74 863-883, (2008)
- Kérchy L., Léka Z., Representations with regular norm-behaviour of locally compact abelian semigroups, Stud. Math.,183, 143-160. (2007).

__Positions:__

__CURRENT POSITION__:

__PREVIOUS POSITIONS__:

01/09/2014 – 31/06/2018 senior lecturer, Budapest Business School

Department of Mathematics, Royal Holloway, University of London

01/09/2011 – 31/08/2014 associate research fellow, MTA Rényi Institute, Hungary

01/09/2009 – 31/07/2011 post-doctoral researcher

01/09/2006 – 31/08/2009 funded research assistant