Products of m-isometries

被引：55
作者：
Bermudez, Teresa [1 ]
Martinon, Antonio [1 ]
Agustin Noda, Juan [1 ]
机构：
[1] Univ La Laguna, Dept Anal Matemat, San Cristobal la Laguna 38271, Tenerife, Spain
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 01期
关键词：
Isometry; m-Isometry; (m; p)-Isometry; Hilbert-Schmidt operators; OPERATORS; TRANSFORMATIONS; THEOREM;
D O I：
10.1016/j.laa.2012.07.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An operator Ton a Banach space X is called an (m, p)-isometry if it satisfies the equality Sigma(m)(k=0) ((m)(k))(-1)(m-k)parallel to T(k)x parallel to(p) = 0, for all x epsilon X. In this paper we prove that if T is an (n, p)-isometry, S is an (m, p)-isometry and they commute, then TS is an (m + n - 1, p)-isometry. This result applied to elementary operators of length 1 defined on the Hilbert-Schmidt class proves a conjecture in [11]. (C) 2012 Elsevier Inc. All rights reserved.
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页码：80 / 86
页数：7
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