Completely bounded norms of right module maps

Files in This Item:
File Description SizeFormat 
rightmod-arxiv2.pdf408.9 kBAdobe PDFDownload
Title: Completely bounded norms of right module maps
Authors: Levene, Rupert H.
Timoney, Richard M.
Permanent link:
Date: 1-Mar-2012
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 boundedRight module mapMatrix numerical rangeTracial geometric meanFidelity
DOI: 10.1016/j.laa.2011.08.036
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

Show full item record

Citations 50

Last Week
Last month
checked on Sep 17, 2018

Google ScholarTM



This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.