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My full name coud not fit on the google sites header so I am putting it here: Andriamanankasina Ramanantoanina, but you may know me as Manana. I did my PhD in Mathematics at the Central European University in Budapest (now in Vienna) under the guidance of my advisor, Lajos Molnár. Prior to that, I did my undergraduate studies in Antananarivo, then went to South Africa to do my Masters at the African Institute for Mathematical Sciences and the University of Cape Town. I then took a year off to work as an IT assistant at AIMS in South Africa, where I met my wife, Rojo Randrianomentsoa.
Formal Publications
Formal Publications
Lattice properties of strength functions (doi)
A. Ramanantoanina, T. Titkos;
Acta Scientiarum Mathematicarum (Szeged), (2024).
This paper investigates an important functional representation of the cone of bounded positive semidefinite operators. It is known that the representation by strength functions turns the Löwner order into the pointwise order. However, very little is known about the structure of strength functions. Our main result says that the representation behaves naturally with the infimum and supremum operations. More precisely, we show that the pointwise minimum of two strength functions is a strength function if and only if the infimum of the corresponding operators exists. This complements a recent result of L. Molnár stating that the pointwise maximum of two strength functions is again a strength function if and only if the corresponding operators are comparable, as this latter statement is equivalent to the existence of the supremum. The cornerstone of each argument in this paper is a fact that was discovered recently, namely that the strength function of the parallel sum two operators (which is half of their harmonic mean) equals the parallel sum of the corresponding strength functions. We provide a new proof for this statement, and as a byproduct, in some special cases, we describe the strength function of the so-called (generalized) short.
Characterisation of the lattice operations on positive operators with respect to the spectral order (doi)
A. Ramanantoanina
Linear Algebra and its Applications 656, 446-462 (2023).
Kubo and Ando defined a family of operations on positive operators that are now referred to as Kubo-Ando means. These operations are monotone with respect to the usual order and they satisfy the so called transformer inequality, a property which relates the operations to the usual order and congruence transformations. In this paper, we derive a spectral order analogue of the transformer inequality, and we prove that, essentially, the only operations on positive operators which are monotone with respect to the spectral order and satisfy this new transformer inequality are the join and the meet operations with respect to the spectral order.
On functional representations of positive Hilbert space operators (doi)
L. Molnár, A. Ramanantoanina
Integral Equations and Operator Theory 93 (1),2 (2021).
In this paper we consider some faithful representations of positive Hilbert space operators on structures of nonnegative real functions defined on the unit sphere of the Hilbert space in question. Those representations turn order relations between positive operators to order relations between real functions. Two of them turn the usual Löwner order between operators to the pointwise order between functions, another two turn the spectral order between operators to the same, pointwise order between functions. We investigate which algebraic operations those representations preserve, hence which kind of algebraic structure the representing functions have. We study the differences among the different representing functions of the same positive operator. Finally, we introduce a new complete metric (which corresponds naturally to two of those representations) on the set of all invertible positive operators and formulate a conjecture concerning the corresponding isometry group.
A Gleason solution model for row contractions (doi)
R. T. W. Martin, A. Ramanantoanina
In: Bolotnikov, V., ter Horst, S., Ran, A., Vinnikov, V. (eds) Interpolation and Realization Theory with Applications to Control Theory: In Honor of Joe Ball. Operator Theory: Advances and Applications, vol 272 (2019)
In the de Branges–Rovnyak functional model for contractions on Hilbert space, any completely non-coisometric (CNC) contraction is represented as the adjoint of the restriction of the backward shift to a de Branges– Rovnyak space associated to a contractive analytic operator-valued function on the open unit disk.
We extend this model to a large class of CNC contractions of several copies of a Hilbert space into itself (including all CNC row contractions with commuting component operators). Namely, we completely characterize the set of all CNC row contractions, which are unitarily equivalent to an extremal Gleason solution for a de Branges–Rovnyak space, contractively contained in a vector-valued Drury–Arveson space of analytic functions on the open unit ball in several complex dimensions. Here, a Gleason solution is the appropriate several-variable analogue of the adjoint of the restricted backward shift and the characteristic function, belongs to the several-variable Schur class of contractive multipliers between vector-valued Drury–Arveson spaces. The characteristic function, is a unitary invariant, and we further characterize a natural sub-class of CNC row contractions for which it is a complete unitary invariant.
Other Publications
Other Publications
Positive Hilbert Space Operators as Real Valued Functions
A. Ramanantoanina
Central European University, Hungary (2020).
Practical Mathematics Specialization Program, dissertation [pdf]
Gleason solutions and canonical models for row contractions
A. Ramanantoanina
University of Cape Town, South Africa (2017).
MSc. thesis [pdf]
Multivariable dilation theory
A. Ramanantoanina
Africa Institute for Mathematical Sciences, South Africa (2014).
MSc. research project [pdf]
Talks & Seminars
Talks & Seminars
Preservers weekend, University of Szeged, Hungary, May 2019
Analysis Seminar, University of Szeged, Hungary, December 2019
Talk: Functional representation of positive operators.
PhD Seminar, Central European University, Hungary (Mars 2020)
Talk: Non linear preserver problems on operator algebras
Functional Analysis and Operator Theory Webinar, onine 2020 - 2021
with an emphasis on preserver problems and quantum information.
Zagreb Workshop on Operator Theory (Online, June 2020)
Talk: Positive operators as real valued functions
8th European Congress of Mathematics, Portoroz, Slovenia (Online, June 2021)
MS: Recent Developments on Preservers
Research on preserver problems on Banach algebras and related topics, RIMS (Online, October 2021 )
School on Linear Preserver Problems, IISER Bhopal, India (July 2024)
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