APM  Vol.9 No.11 , November 2019
RETRACTED: Disintegration of Group Representations on Direct Integrals of Banach Spaces

Short Retraction Notice 

The paper does not meet the standards of "Advances in Pure Mathematics". 

This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused. 

Editor guiding this retraction: Editorial Board (EIC of APM). 

Please see the article page for more details. The full retraction notice in PDF is preceding the original paper which is marked "RETRACTED".

Cite this paper:   

[1]   Marcel de Jeu, J.R. (2017) Disintegration of Positive Isometric Group Reresentations on Lp-Space. Positivity, 21, 673-710.

[2]   de Jeu, M. and Messerschmidt, M. (2013) Crossed Products of Banach Algebras. III. Functional Analysis.

[3]   de Jeu, M. and Ruoff, F. (2016) Positive Representations of Co(X), I. Annals of Functional Analysis, 7, 180-205.

[4]   Wickstead, A.W. (2015) Banach Lattice Algebras: Some Questions. Positivity, 21, 803-815.

[5]   Wickstead, A.W. (2017) Two Dimensional Unital Riesz Algebras, Their Representations and Norms. Positivity, 21, 787-801.

[6]   Zaanen, A.C. (1997) Introduction to Operator Theory in Riesz Spaces. Springer, Berlin.

[7]   de Jeu, M. and Wortel, M. (2012) Positive Representations of Finite Groups in Riesz Spaces. International Journal of Mathematics, 23, Article ID: 1250076.

[8]   de Jeu, M. and Wortel, M. (2014) Compact Groups of Positive Operators on Banach Lattices. Indagationes Mathematicae, 25, 186-205.

[9]   Eisner, T., Farkas, B., Haase and Nagel, R. (2015) Operator Theoretic Aspects of Ergodictheory. In: Graduate Texts in Mathematics, Springer, Berlin.

[10]   Kechris, A.S. (1995) Classical Descriptive Set Theory. In: Graduate Texts in Mathematics, Springer, Berlin.

[11]   Becker, H. and Kechris, A.S. (1996) The Descriptive Set Theory of Polish Group Actions. Cambridge University Press, Cambridge.

[12]   Bogachev, V.I. (2007) Measure Theory. Springer, Berlin.

[13]   Haydon, R., Levy, M. and Raynaud, Y. (1991) Randomly Normed Spaces. In: Travauxen Cours (Works in Progress), Volume 41, Springer, Berlin, Hermann.

[14]   Folland, G.B. (1995) A Course in Abstract Harmonic Analysis. In: Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.

[15]   Aliprantis, C.D. and Burkinshaw, O. (1998) Principles of Real Analysis. Academic Press, Inc., London.

[16]   Nevo, A. (2006) Pointwise Ergodic Theorems for Actions of Groups. In: Hasselblatt, B. and Katok, A., Eds., Handbook of Dynamical Systems, Elsevier B.V., New York, 871-982.

[17]   Ryan, R.A. (2002) Introduction to Tensor Products of Banach Spaces. In: Springer Monographs in Mathematics, Springer, London.

[18]   Cohn, D.L. (1993) Measure Theory. Birkhauser, Boston, MA.

[19]   Zakrzewski, P. (2002) Measures on Algebraic-Topological Structures. In: Pap, E., Ed., Handbook of Measure theory, Volume I, II, Elsevier, New York, 1091-1130.

[20]   Fleming, R.J. and Jamison, J.E. (2003) Isometries on Banach Spaces: Function Spaces. In: Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, Volume 129, Chapman & Hall/CRC, Boca Raton, FL.

[21]   Joseph, S., Mukhtar, I. and Juma, M. (2018) The Series of Semigroup Theory via Functional Calculus. American Research Journal of Mathematics, 4, 1-17.