Isometric dilations and von Neumann inequality for a class of tuples in the polydisc
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- by Sibaprasad Barik, B. Krishna Das, Kalpesh J. Haria and Jaydeb Sarkar PDF
- Trans. Amer. Math. Soc. 372 (2019), 1429-1450 Request permission
Abstract:
The celebrated Sz.-Nagy and Foias and Ando theorems state that a single contraction, or a pair of commuting contractions, acting on a Hilbert space always possesses isometric dilation and subsequently satisfies the von Neumann inequality for polynomials in $\mathbb {C}[z]$ or $\mathbb {C}[z_1, z_2]$, respectively. However, in general, neither the existence of isometric dilation nor the von Neumann inequality holds for $n$-tuples, $n \geq 3$, of commuting contractions. The goal of this paper is to provide a taste of isometric dilations, von Neumann inequality, and a refined version of von Neumann inequality for a large class of $n$-tuples, $n \geq 3$, of commuting contractions.References
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Additional Information
- Sibaprasad Barik
- Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
- Email: sibaprasadbarik00@gmail.com
- B. Krishna Das
- Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
- MR Author ID: 999492
- Email: dasb@math.iitb.ac.in, bata436@gmail.com
- Kalpesh J. Haria
- Affiliation: School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175005, Himachal Pradesh, India
- MR Author ID: 1037705
- ORCID: setImmediate$0.43056093711685606$1
- Email: kalpesh@iitmandi.ac.in, hikalpesh.haria@gmail.com
- Jaydeb Sarkar
- Affiliation: Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India
- MR Author ID: 773222
- Email: jay@isibang.ac.in, jaydeb@gmail.com
- Received by editor(s): November 1, 2017
- Received by editor(s) in revised form: June 18, 2018
- Published electronically: April 4, 2019
- Additional Notes: The research of the first author is supported by Council of Scientific & Industrial Research (CSIR) Fellowship
The research of the second author is supported by DST-INSPIRE Faculty Fellowship No. DST/INSPIRE/04/2015/001094
The research work of the third author is supported by DST-INSPIRE Faculty Fellowship No. DST/INSPIRE/04/2014/002624
The research of the fourth author is supported in part by Mathematical Research Impact Centric Support (MATRICS) grant, File No : MTR/2017/000522, by the Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India, and NBHM (National Board of Higher Mathematics, India) Research Grant NBHM/R.P.64/2014 - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 1429-1450
- MSC (2010): Primary 47A13, 47A20, 47A45, 47A56, 46E22, 47B32, 32A35, 32A70
- DOI: https://doi.org/10.1090/tran/7676
- MathSciNet review: 3968807