Abstract
Inspired by recent works on (m, C)-isometric and [m, C]-isometric operators on Hilbert spaces studied respectively in Chō et al. (Complex Anal. Oper. Theory 10:1679–1694, 2016; Filomat 31:7, 2017), in this paper we introduce the class of (m, C)-isometries for tuple of commuting operators. This is a generalization of the class of (m, C)-isometric operators. A commuting tuples of operators \(\mathbf{\large T}=(T_1,\ldots ,T_d)\in {\mathcal {B}}^{(d)}({\mathcal {H}})\) is said to be (m, C)-isometric tuple if
for some positive integer m and some conjugation C. We consider a multivariable generalization of these single variable (m, C)-isometric operators and explore some of their basic properties.
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Acknowledgements
This research is partially supported by Grant-in-Aid Scientific Research No.15K04910. The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2016R1A2B4007035).
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Ahmed Mahmoud, S.A.O., Chō, M. & Lee, J.E. On \(\varvec{(m,C)}\)-Isometric Commuting Tuples of Operators on a Hilbert Space. Results Math 73, 51 (2018). https://doi.org/10.1007/s00025-018-0810-0
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DOI: https://doi.org/10.1007/s00025-018-0810-0