Title: Additive Units of Product System of Hilbert Modules
Author(s): Biljana Vujosevic
Pages: 71-76
Cite as:
Biljana Vujosevic, Additive Units of Product System of Hilbert Modules, Int. J. Anal. Appl., 10 (2) (2016), 71-76.

Abstract


In this paper we consider the notion of additive units and roots of a central unital unit in a spatial product system of two-sided Hilbert C∗-modules. This is a generalization of the notion of additive units and roots of a unit in a spatial product system of Hilbert spaces introduced in [B. V. R. Bhat, M. Lindsay, M. Mukherjee, Additive units of product system, arXiv:1501.07675v1 [math.FA] 30 Jan 2015]. We introduce the notion of continuous additive unit and continuous root of a central unital unit ω in a spatial product system over C∗-algebra B and prove that the set of all continuous additive units of ω can be endowed with a structure of two-sided Hilbert B − B module wherein the set of all continuous roots of ω is a Hilbert B − B submodule.

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References


  1. B. V. R. Bhat, Martin Lindsay and Mithun Mukherjee, Additive units of product system, arXiv:1501.07675v1 [math.FA] 30 Jan 2015.

  2. S. D. Barreto, B. V. R. Bhat, V. Liebscher and M. Skeide, Type I product systems of Hilbert modules, J. Funct. Anal. 212 (2004), 121–181.

  3. B. V. R. Bhat and M. Skeide, Tensor product systems of Hilbert modules and dilations of completely positive semigroups, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (2000), 519–575.

  4. D. J. Keˇcki´c, B. Vujoˇsevi´c, On the index of product systems of Hilbert modules, Filomat, 29 (2015), 1093-1111.

  5. E. C. Lance, Hilbert C∗-Modules: A toolkit for operator algebraists, Cambridge University Press, (1995).

  6. V. M. Manuilov and E. V. Troitsky, Hilbert C∗-Modules, American Mathematical Society (2005).

  7. M. Skeide, Dilation theory and continuous tensor product systems of Hilbert modules, PQQP: Quantum Probability and White Noise Analysis XV (2003), World Scientific.

  8. M. Skeide, Hilbert modules and application in quantum probability, Habilitationsschrift, Cottbus (2001).

  9. M. Skeide, The index of (white) noises and their product systems, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9 (2006), 617–655.