Norms of idempotent Schur multipliers

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Title: Norms of idempotent Schur multipliers
Authors: Levene, Rupert H.
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Date: 7-Apr-2014
Abstract: Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers η0 < η1 < η2 < · · · < η6 so that for every bounded, normal D-bimodule map Φ on B(H), either kΦk > η6 or kΦk = ηk for some k ∈ {0, 1, 2, 3, 4, 5, 6}. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm ηk for 0 ≤ k ≤ 6. We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n × n matrix, or of an n×(n+ 1) matrix, both have norm 2 n+1 cot(π 2(n+1) ), and we consider the average norm of a random idempotent Schur multiplier as a function of dimension. Many of our arguments are framed in the combinatorial language of bipartite graphs.
Type of material: Journal Article
Publisher: Electronic Journal Project
Copyright (published version): 2014 the Author
Keywords: Idempotent Schur multiplierNormal masa bimodule mapHadamard productNormBipartite graph
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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