arXiv subjects

Fernanda Botelho

Publications and source records attributed to Fernanda Botelho.

6 recordsLinked to original sources

arXiv2026

On Nonlinear Idempotents and Metric Projections in Normed Spaces

Let $X$ be a normed linear space. A map $P: X \rightarrow X$ is called idempotent if $P^2 = P$. In this paper, we introduce some new classes of idempotent maps (linearity is not assumed) on $X$ and study their properties. A well-known example of an idempotent map is the metric projection $P_K$ onto a Chebyshev subset $K$ of $X$. We provide some necessary conditions for the map $I- P_K$ to be idempotent, where $I$ denotes the identity operator on $X$.

math.FA↗

arXiv2026

Generalized idempotents on the space of analytic functions with bounded derivatives

Let $X$ be a complex normed space. A map $P: X \rightarrow X$ is called idempotent if $P^2 = P$. A collection $\mathcal{C} = \{P_1, P_2\}$ of nonzero distinct orthogonal ($P_1P_2 = P_2P_1 = 0$) idempotent maps on $X$ is said to be a family of generalized bi-circular idempotents if there exist distinct unit modulus complex numbers $\lambda_1, \lambda_2$ such that $P_1 + P_2 = I$ (identity operator on $X$) and $\lambda_1P_1 + \lambda_2P_2$ is a surjective isometry on $X$. This generalizes the notion of generalized bi-circular projections on Banach spaces introduced by Fo\v{s}ner, Ili\v{s}evi\'{c} and Li \cite{MDC} to nonlinear maps. In this paper, we describe the structure of generalized bi-circular idempotents over the space of analytic functions on the open unit disk with bounded derivatives.

math.FA↗

arXiv2021

The Existence of Linear Selection and the Quotient Lifting Property

Lifting properties for Banach spaces are studied. An alternate version of the lifting property due to Lindenstrass and Tzafriri is proposed and a characterization, up to isomorphism, is given. The quotient lifting property for pairs of Banach spaces $(X,J)$, with $J$ proximinal in $X$, is considered and several conditions for the property to hold are given.

math.FA↗

arXiv2014

Isometries and Hermitian operators on $\mathcal{B}_0(\triangle, E)$

In this paper we describe the surjective linear isometries on a vector valued little Bloch space with range space a strictly convex and smooth complex Banach space. We also describe the hermitian operators and the generalized bi-circular projections supported by these spaces.

math.FA↗

arXiv2014

Isometries and Hermitian Operators on Zygmund spaces

In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.

math.FA↗

arXiv2012

Representation of Generalized Bi-Circular Projections on Banach Spaces

We prove several results concerning the representation of projections on arbitrary Banach spaces. We also give illustrative examples including an example of a generalized bi-circular projection which can not be written as the average of the identity with an isometric reflection. We also characterize generalized bi-circular projections on $C_0(\Om,X)$, with $\Om$ a locally compact Hausdorff space (not necessarily connected) and $X$ a Banach space with trivial centralizer.

math.FA↗