Options
Norms of idempotent Schur multipliers
Author(s)
Date Issued
2014-04-07
Date Available
2014-11-10T16:56:34Z
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
Journal
New York Journal of Mathematics
Volume
20
Issue
2014
Start Page
325
End Page
352
Copyright (Published Version)
2014 the Author
Web versions
Language
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
File(s)
Owning collection
Views
1363
Last Month
1
1
Acquisition Date
Mar 28, 2024
Mar 28, 2024
Downloads
122
Last Month
2
2
Acquisition Date
Mar 28, 2024
Mar 28, 2024