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Advances in Mathematical Physics

Volume 2011 (2011), Article ID 272703, 1 page

http://dx.doi.org/10.1155/2011/272703

## Erratum to “The Partial Inner Product Space Method: A Quick Overview”

^{1}Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium^{2}Dipartimento di Matematica ed Applicazioni, Università di Palermo, 90123, Italy

Received 27 February 2011; Accepted 13 March 2011

Copyright © 2011 Jean-Pierre Antoine and Camillo Trapani. 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.

The definition of homomorphism given in Section 5.2.2 is incorrect. Here is the exact definition. The rest of the discussion is correct.

Let be two LHSs or LBSs. An operator is called a*homomorphism*if(i)for every , there exists such that both and exist;(ii)for every , there exists such that both and exist.

Equivalently, for every , there exists such that and , and for every , there exists with the same property.

The definition may be rephrased as follows: is a homomorphism if where and , denote the projection on the first, respectively, the second component.

Contrary to what is stated in [1, Definition 3.3.4], the condition (1), which is the correct one, does *not* imply and .

We denote by the set of all homomorphisms from into . The following property is easy to prove:

Let . Then, implies .

#### References

- J.-P. Antoine and C. Trapani,
*Partial Inner Product Spaces—Theory and Applications*, vol. 1986 of*Springer Lecture Notes in Mathematics*, Springer, Berlin, Germany, 2010.