Some geometric properties on Banach spaces associated to hypergroups.

• Author / Creator

  Tahmasebi, Nazanin

• This thesis is dedicated to the study of some geometric properties on Banach spaces associated to hypergroups. This thesis contains three major parts.

  The purpose of the first part is to initiate a systematic approach to the study of the class of invariant complemented subspaces of L∞(K), and C0(K), the class of left translation invariant W-subalgebras of L∞(K) and finally the class of non-zero left translation invariant C-subalgebras of C0(K) in the hypergroup context with the goal of finding some relations between these function spaces.

  The second part consists of two themes; fixed point properties for non-expansive and affine maps. The first theme provides a condition when a non-expansive self map on a weak (weak*) compact convex subset of several function spaces over K has a fixed point while the second theme present some applications of common fixed point properties for affine actions of K.

  The main concentration of the third part is on initiating the study of inner amenable hypergroups extending amenable hypergroups and inner amenable locally compact groups.

• Subjects / Keywords

  • Inner Amenable
  • Amenable
  • Geometric properties on Banach spaces
  • Hypergroups

• Graduation date

  Fall 2015

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R35D8NM0H

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.