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 -