List of Published Papers:
Franca, W. , Emerick, P. On (Non)Lineability of Some Subsets of l_1 . Bull Braz Math Soc, New Series 57, 3 (2026). https://doi.org/10.1007/s00574-025-00493-0
Franca, Willian; Louza, Nelson. Commuting maps on idempotents and Functional Identities on finite subsets of fields, Linear Multilinear Algebra. 72(15), 2539–2554, 2024 (https://www.tandfonline.com/doi/full/10.1080/03081087.2023.2271640)
FRANCA, WILLIAN; MENEGATTO, V. A. Positive definite functions on products of metric spaces by integral transforms. Journal of Mathematical Analysis and Applications, 2022. (https://doi.org/10.1016/j.jmaa.2022.126304 )
FRANCA, WILLIAN; MENEGATTO, V. A. Stricly Positive definite functions by integral transforms. Expositiones Mathematicae, 2022. (https://doi.org/10.1016/j.exmath.2022.05.001 )
FRANCA, WILLIAN; DE MORAES, LUIZA. On the spectrum of a class of non-commutative Banach algebras. Archiv der Mathematik, 2022. (https://link.springer.com/article/10.1007/s00013-022-01713-5)
FRANCA, WILLIAN; MENEGATTO, V. A. Matrix-valued positive definite kernels given by expansions: strict positive definiteness. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2021. (http://mia.ele-math.com/24-79/Matrix-valued-positive-definite-kernels-given-by-expansions-strict-positive-definiteness)
FRANCA, WILLIAN; ALVES, M. B. Linear transformations preserving algebraic elements of degree 2. Linear & Multilinear Algebra, 2021. (https://doi.org/10.1080/03081087.2021.1873228 )
URURE, R. I. Q. ; FRANCA, W. Lvov-Kaplansky conjecture on UT_m^+ with the transpose involution. Operators and Matrices, v. 15, p. 175-193, 2021. (https://doi.org/10.1080/03081087.2020.1849006)
FRANCA, WILLIAN; LOUZA, NELSON . Power commuting traces of bilinear maps on invertible elements. Journal of Algebra and its Applications, v. -, p. 2150023--, 2021.
URURE, R. I. Q ; FRANCA, WILLIAN . Lie identities and images of Lie polynomials for the skew-symmetric elements of UT m . Linear & Multilinear Algebra, v. -, p. 1-17, 2020.(https://doi.org/10.1080/03081087.2020.1849006)
FRANCA, WILLIAN; LOUZA JUNIOR, N. D. . Generalized commuting maps on the set of singular matrices. THE ELECTRONIC JOURNAL OF LINEAR ALGEBRA, v. 35, p. 533-542, 2019.
FRANCA, WILLIAN. Commuting traces of Multilinear maps on invertible elements. Communications in Algebra, v. 46, p. 2890-2898, 2018.
FRANCA, WILLIAN. Weakly commuting maps on the set of rank-1 matrices. Linear and Multilinear Algebra, v. 65, p. 475-495, 2017.
FRANÇA, W. V.; LOUZA JUNIOR, N. D. . Commuting maps on rank-1 matrices over noncommutative division rings. COMMUNICATIONS IN ALGEBRA, v. 45, p. 4696-4706, 2017.
FRANCA, WILLIAN. Commuting Traces of Biadditive Maps on Invertible Elements. Communications in Algebra, v. 44, p. 2621-2634, 2016.
FRANÇA, W. V.. Commuting traces on invertible and singular operators. Operators and Matrices, v. 9, p. 305-310, 2015.
FRANCA, WILLIAN. Commuting traces of multiadditive maps on invertible and singular matrices. Linear and Multilinear Algebra, v. 61, p. 1528-1535, 2013.
FRANCA, WILLIAN. Commuting maps on rank-k matrices. Linear Algebra and its Applications, v. 438, p. 2813-2815, 2013.
FRANCA, WILLIAN. Commuting maps on some subsets of matrices that are not closed under addition. Linear Algebra and its Applications, v. 437, p. 388-391, 2012.
Preprints:
Franca, W., Jorge J. Garcés Applications of compact multipliers to algebrabrility of (ℓ∞ \ c0) ∪ {0} and (B(ℓ2(N)) \ K(ℓ2(N)) ∪ {0}. (2025)
Papers Accepted for Publication: