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Completely bounded norms of right module maps

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Download rightmod-arxiv2.pdf408.9 KB
Author(s)
Levene, Rupert H. 
Timoney, Richard M. 
Uri
http://hdl.handle.net/10197/6158
Date Issued
01 March 2012
Date Available
13T09:14:56Z November 2014
Abstract
It is well-known that if T is a Dm–Dn bimodule map on the m×n complex matrices, then T is a Schur multiplier and kTkcb = kTk. If n = 2 and T is merely assumed to be a right D2-module map, then we show that kTkcb = kTk. However, this property fails if m ≥ 2 and n ≥ 3. For m ≥ 2 and n = 3, 4 or n ≥ m2 we give examples of maps T attaining the supremum C(m, n) = sup{kTkcb : T a right Dn-module map on Mm,n with kTk ≤ 1}, we show that C(m, m2) = √ m and succeed in finding sharp results for C(m, n) in certain other cases. As a consequence, if H is an infinite-dimensional Hilbert space and D is a masa in B(H), then there is a bounded right D-module map on K(H) which is not completely bounded.
Type of Material
Journal Article
Publisher
Elsevier
Journal
Linear Algebra and Its Applications
Volume
436
Issue
5
Start Page
1406
End Page
1424
Copyright (Published Version)
2011 Elsevier
Keywords
  • Completely bounded

  • Right module map

  • Matrix numerical rang...

  • Tracial geometric mea...

  • Fidelity

DOI
10.1016/j.laa.2011.08.036
Language
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
Owning collection
Mathematics and Statistics Research Collection
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2
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Feb 6, 2023
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