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TZID:America/Chicago
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DTSTART:20211107T020000
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DTSTART:20220313T020000
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BEGIN:VEVENT
UID:calendar.25179.field_event_date_2.0@math.wustl.edu
CREATED:20211028T161758Z
DESCRIPTION:Abstract: Spectral sets and K-spectral sets, introduced by Joh
n von Neumann in 1951, offer a possibility to estimate the norm of functi
ons of matrices in terms of the supremum norm of the function. The concep
t of spectral sets is partially motivated by von Neumann’s inequality, wh
ich can be interpreted as saying that a Hilbert space operator T is a cont
raction if and only if the closed unit disk is a spectral set for T. In th
is expository talk, we discuss recent progress on a famous open problem i
n this area, the so-called Crouzeix's conjecture: the closure of the nume
rical range W(T) of every operator T is 2-spectral for T. We will begin by
looking at some fundamental properties of W(T) and then analyze the recen
t Crouzeix-Palencia proof that W(T) is always $(1+\sqrt{2})$-spectral. Par
tial answers to the conjecture, the role of associated 'extremal function
s' and ways to extend the Crouzeix-Palencia proof to domains that do not n
ecessarily contain W(T) will also be discussed.\n\nHost: John McCarthy
DTSTART;TZID=America/Chicago:20211108T150000
DTEND;TZID=America/Chicago:20211108T160000
LAST-MODIFIED:20211028T161920Z
SUMMARY:Analysis Seminar/Third Year Requirement: 'K-spectral sets and Crouz
eix’s Conjecture'
URL;TYPE=URI:https://math.wustl.edu/events/analysis-seminarthird-year-requi
rement-k-spectral-sets-and-crouzeix%E2%80%99s-conjecture
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