Advances in Mathematical Physics
Volume 2011 (2011), Article ID 957592, 22 pages
http://dx.doi.org/10.1155/2011/957592
Research Article

Partial Inner Product Spaces: Some Categorical Aspects

Jean-Pierre Antoine,1 Dominique Lambert,2 and Camillo Trapani3

1Institut de Recherche en Mathématique et Physique (IRMP), Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
2Dipartimento di Matematica e Informatica, Università di Palermo, 90123 Palermo, Italy
3Namur Center for Complex Systems (NAXYS), Facultés Universitaires Notre-Dame de la Paix, B-5000 Namur, Belgium

Received 16 March 2011; Revised 20 July 2011; Accepted 10 August 2011

Academic Editor: Partha Guha

Copyright © 2011 Jean-Pierre Antoine et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces ( 𝖯 𝖨 𝖯 -spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain 𝖯 𝖨 𝖯 -spaces of practical interest.