index.Rmd

--- 
title: "Symmetry and spectral invariance for topologically graded C*‐algebras and partial action systems"
author: "Diego Jauré"
#date: "`r Sys.Date()`"
site: bookdown::bookdown_site
documentclass: book
bibliography: [book.bib, packages.bib]
# url: your book url like https://bookdown.org/yihui/bookdown
# cover-image: path to the social sharing image like images/cover.jpg
description: |
  This is a minimal example of using the bookdown package to write a book.
  The HTML output format for this example is bookdown::gitbook,
  set in the _output.yml file.
link-citations: yes
github-repo: rstudio/bookdown-demo
---

# Abstract {-}

The main focus of this thesis is to show that in each topologically graded $C^*$-algebra over a rigidly symmetric group there is a $\ell^1$-type symmetric Banach $^*$-algebra,which is inverse closed in the $C^*$-algebra. This includes new general classes, as algebras admitting dual actions and partial crossed products. Results including convolution dominated kernels, inverse closedness with respect with ideals or weighted versions of the $\ell^1$-decay are included. Various concrete examples are also presented. Finally the symmetry of Fell bundles over groupoids is studied, where in the case of a discrete groupoid the notions of rigid symmetry and hypersymmetry coincide.

# Agradecimientos {-}

Dedicado a mis padres, mi hermana y Fabián. No es posible imaginar una mejor vida sin el apoyo incondicional recibido por parte de ellos.

Quiero dar las gracias a quienes me acompañaron en el camino. En particular, agradecer a Anabelén, a los miembros de Bourbaki y a las bellas amistades que pude hacer en la facultad. Ustedes llenan mi memoria de buenos recuerdos durante los momentos difíciles.

Por último, quiero agradecer a Marius M\v{a}ntoiu por su infinita paciencia y disposición.