## Areas of Expertise

Matrix analysis; Quantum groups; Operator algebras

## Education

Ph.D. Mathematics

University of Cincinnati, 2007

B.S. Mathematics

University of Bucharest, 2002

## Biography

## Awards

McMicken Outstanding Doctoral Student Award

University of Cincinnati, 2007

Charles Phelps Taft Dissertation Fellowship

University of Cincinnati, 2005

Taft Graduate Enrichment Award

University of Cincinnati, 2005

Isabel and Mary Neff Scholarship

University of Cincinnati, 2004

Summer Graduate Student Research Fellowship

University of Cincinnati, 2004

Taft Graduate Enhancement Fellowship

University of Cincinnati, 2002-2004

** **

## Grants and Contracts Awarded

Faculty development research grant

University of North Florida, 2008

Taft Graduate Student Travel grant

University of Cincinnati, 2007

## Publications & Presentations

**Published:**

- "Some geometric properties of matrix means in different distance functions", T. Hoa Dinh, R. Dumitru, and J. Franco (to appear in
*Positivity*). - "On the matrix heron means and Renyi Divergences", T. Hoa Dinh, R. Dumitru, and J. Franco (to appear in
*Linear Multilinear Algebra*). - "Generalized Hellinger Metrics and Audenaert's In-Betweenness", R. Dumitru, J. Franco,
*Linear Algebra and its Applications, 585 (2020), 191 - 198*. - "On some trace inequalities", T. Hoa Dinh, R. Dumitru, and J. Franco,
*Mathematical Inequalities & Applications, 23(2), (2020), 467- 476*. - "Longitudinal Dynamic Functional Regression", A. M. Staicu, Md N. Islam, R. Dumitru, Eric van Heugten,
*Journal of the Royal Statistical Society Series C*, Royal Statistical Society, vol. 69(1), (2020), 25-46. - "Fundamental Theorems of Summability Theory for a New Type of Subsequences of Double Sequences", R. Dumitru, J.Franco,
*Journal of Classical Analysis,*15(1), (2019), 23- 33. - "Non-Linear Interpolation of the Harmonic-Geometric-Arithmetic Matrix Means", T. Hoa Dinh, R. Dumitru, and J. Franco,
*Lobachevskii Journal of Mathematics*, 40(1), (2019), 101-106. - “The matrix power means and interpolations”, Trung Hoa Dinh, R. Dumitru, and J. Franco,
*Advances in Operator Theory*, Vol.3, Nr. 3 (2018), 647-654. - “New characterizations of operator monotone functions”, Trung Hoa Dinh, R. Dumitru, and J. Franco,
*Linear Algebra and its Applications,*546 (2018), 169-186. - “On a q-analogue of Hilbert's inequality”, R. Dumitru and J. Franco,
*Electronic Journal of Math. Analysis and Applications*, Vol. 6(2) (2018), 279-287. - “On a conjecture of Bhatia, Lim and Yamazaki”, Trung Hoa Dinh, R. Dumitru, and J. Franco,
*Linear algebra and its Applications*, Vol. 532 (2017), 140-145. - “On the monotonicity of weighted power means of matrices”, Trung Hoa Dinh, R. Dumitru and J. Franco,
*Linear Algebra and its Applications*, 527 (2017), 128-140. - “On singular value inequalities for matrix means” R. Dumitru, R. Levanger, B. Visinescu,
*Linear Algebra and its Applications*, Vol 439, 8(2013), 2405-2410. - “Nuclear and type I crossed products of C*-algebras by group and compact quantum group actions” R. Dumitru, C. Peligrad,
*Journal of Operator Theory*, 69(2013), 287-296. - “Spectra for compact quantum group actions and crossed products” R. Dumitru, C. Peligrad,
*Transactions of the American Math. Society*, 364(2012), 3699-3713. - “Reflexivity of operator algebras of finite split strict multiplicity” R. Dumitru, C. Peligrad, B. Visinescu,
*Operators and Matrices*, 5(2011), 221-226. - “Simple and Prime crossed products of C*-algebras by compact quantum group coactions” R. Dumitru,
*Journal of Functional Analysis*257 (2009), 1480-1492. - “Unitary representations of compact quantum groups”, R. Dumitru, Perspectives in
*Operator Algebras and Math. Physics*, 85-90. - “Compact Quantum group actions on C*-algebras and invariant derivations” R. Dumitru, C. Peligrad,
*Proc. Amer. Math. Soc*., Vol. 135, No. 12 (2007), 3977-3984. - “Automorphisms inner in the Local Multiplier Algebra and the Connes Spectrum” R. Dumitru, C. Peligrad, B. Visinescu,
*Operator Theory 20*, Proc. 20^{th}International Conf. on Operator Theory, Timisoara, 2004, 75-80.

**In progress:**

1. "Regular Methods of Summability and the Banach-Saks Property for Double Sequences", R. Dumitru, J. Franco, R. Patterson (in preparation)

2. "Matrix Means and Uncertainty Principle Functions", R. Dumitru, J. Franco, F. Zhang (submitted)

3. "On the uniform convexity of the q-analogues of L_{p}spaces and q-Clarkson inequalities", P. Morales, R. Dumitru, and J. Franco, to appear, *International Journal of Nonlinear Science.*