Completely bounded norms of right module maps

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Title: Completely bounded norms of right module maps
Authors: Levene, Rupert H.
Timoney, Richard M.
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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
Copyright (published version): 2011 Elsevier
Keywords: Completely bounded;Right module map;Matrix numerical range;Tracial geometric mean;Fidelity
DOI: 10.1016/j.laa.2011.08.036
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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