arXiv subjects

Jacqueline Ojeda

Publications and source records attributed to Jacqueline Ojeda.

3 recordsLinked to original sources

arXiv2017

Representation theorems for operators on free Banach spaces of type countable

This work will be centered in commutative Banach subalgebras of the algebra of bounded linear operators defined on a Free Banach spaces of countable type. The main goal of this work wil be to formulate a representation theorem for these operators through integrals defined by spectral measures type. In order to get this objective, we will show that, under special conditions, each one of these algebras is isometrically isomorphic to some space of continuous functions defined over a compact set. Then, we will identify such compact developing the Gelfand space theory in the non-archimedean setting. This fact will allow us to define a measure which is known as spectral measure. As a second goal, we will formulate a matrix representation theorem for this class of operators whose entries of these matrices will be integrals coming from scalar measures.

math.FA↗

arXiv2015

Spectral measures over c-algebras of operators defined in $c_0$

The main goal of this work is to introduce an analogous in the non-archimedean context of the Gelfand spaces of certain Banach commutative algebras with unit. In order to do that, we study the spectrum of this algebras and we show that, under special conditions, these algebras are isometrically isomorphic to certain spaces of continuous functions defined over compacts. Such isometries preserve projections and allow to define associated measures which are known as spectral measures. We also show that each element of the algebras can be represented as an integral defined by these measures.

math.FA↗

arXiv2011

p-adic meromorphic functions f'P'(f), g'P'(g) sharing a small function

Let K be a complete algebraically closed p-adic field of characteristic zero. Let f, g be two transcendental meromorphic functions in the whole field K or meromorphic functions in an open disk that are not quotients of bounded analytic functions. Let P be a polynomial of uniqueness for meromorphic functions in K or in an open disk and let $α$ be a small meromorphic function with regards to f and g. If f'P'(f) and g'P'(g) share $α$ counting multiplicity, then we show that f=g provided that the multiplicity order of zeroes of P' satisfy certain inequalities. If $α$ is a Moebius function or a non-zero constant, we can obtain more general results on P.

math.NT↗