On reproducing property and 2-cocycles

Saeed Hashemi Sababe, Ali Ebadian, Shahram Najafzadeh


In this paper, we study reproducing kernels whose ranges are subsets of a $C^*$-algebra or a Hilbert $C^*$-module. In particular, we show how such a reproducing kernel can naturally be expressed in terms of operators on a Hilbert $C^*$-module. We focus on relative reproducing kernels and extend this concept to such spaces associated with cocycles.


reproducing kernel; 2-semi inner product; 2-semi norm

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J. G. Christensen, A. H. Darweesh and G. Olafsson, Coorbits for projective representations with an application to Bergman spaces,arXiv:1704.02522v1 [math.FA], 2017.

M. Frank and D.R. Larson, Frames in Hilbert $C^*$-modules and $C^*$-algebras, J. Operator theory,48 (2002), 273--314.

S. Hashemi Sababe and Ali. Ebadian, Some properties of reproducing kernel Banach and Hilbert spaces.

Sahand Communications in Mathematical Analysis. http://scma.maragheh.ac.ir/article_27822.html(2017). Accessed 11 October 2017.

J. Heo, Reproducing kernel Hilbert -modules and kernels associated with cocycles, Journal of Mathematical Physics,49(2008), 103507--103519.

M. H Hsu and N. C Wong, Inner products and module maps of Hilbert $C^* $-modules, Preprints.

DOI: http://dx.doi.org/10.5556/j.tkjm.49.2018.2553

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