TY - JOUR
T1 - Isometric dilations and von Neumann inequality for a class of Tuples in the polydisc
AU - Barik, Sibaprasad
AU - Krishna Das, B.
AU - Haria, Kalpesh J.
AU - Sarkar, Jaydeb
N1 - Funding Information:
Received by the editors November 1, 2017, and, in revised form, June 18, 2018. 2010 Mathematics Subject Classification. Primary 47A13, 47A20, 47A45, 47A56, 46E22, 47B32, 32A35, 32A70. Key words and phrases. Hardy space over the polydisc, commuting contractions, commuting isometries, isometric dilations, bounded analytic functions, von Neumann inequality, distinguished variety. 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.
Funding Information:
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.
Publisher Copyright:
© 2019 American Mathematical Society.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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 C[z] or C[z1, z2], respectively. However, in general, neither the existence of isometric dilation nor the von Neumann inequality holds for n-tuples, n ≥ 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≥3, of commuting contractions.
AB - 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 C[z] or C[z1, z2], respectively. However, in general, neither the existence of isometric dilation nor the von Neumann inequality holds for n-tuples, n ≥ 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≥3, of commuting contractions.
KW - Bounded analytic functions
KW - Commuting contractions
KW - Commuting isometries
KW - Distinguished variety
KW - Hardy space over the polydisc
KW - Isometric dilations
KW - Von Neumann inequality
UR - http://www.scopus.com/inward/record.url?scp=85070306063&partnerID=8YFLogxK
U2 - 10.1090/tran/7676
DO - 10.1090/tran/7676
M3 - Article
AN - SCOPUS:85070306063
SN - 0002-9947
VL - 372
SP - 1429
EP - 1450
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -