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DTSTART:20191027T020000
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UID:calendar.92352.field_date.0@mathematics.huji.ac.il
DTSTAMP:20200606T113837Z
CREATED:20190917T220019Z
DESCRIPTION:Date: \n\n12:00pm to 1:00pm\n\n\n\n\nSee also: Analysis\, Eve
nts & Seminars\, SeminarsLocation: \n\nRoss 70\n\n\n\nTitle: On the matrix
range of random matrices\nAbstract: In operator theory\, one often attach
es to an operator (or to a family of operators) certain invariants by whic
h the operator can be understood. The spectrum $\sigma(A)$ of an operator
$A$ is an obvious example. Another classical example\, which is somewhat l
ess familiar\, is the numerical range of an operator: it is the set of all
complex numbers obtained from the operator by applying a vector state to
it. Unlike the spectrum\, the notion of numerical range easily extends to
families of operators: the numerical range of a d-tuple $A = (A_1\, \ldots
\, A_d)$ is the collection of all tuples of complex numbers of the form $(
\phi(A_1)\, \ldots\, \phi(A_d))$\, where $\phi$ is a state. It is a subset
of the d-dimensional space\, which carries some information about $A$. \n
My talk will be about a matrix-valued analogue of the numerical range\, ca
lled the matrix range of an operator tuple. I will explain what is the mat
rix range\, what it is good for\, and then I will report on recent work in
which we prove that there is a certain 'universal' matrix range\, to whic
h the matrix ranges of a sequence of large random matrices tends to\, almo
st surely. In particular\, our results imply that the numerical range of a
sequence of certain N-by-N random matrices tends in the Hausdorff metric
to the closed disc as N goes to infinity\, almost surely. The key novel te
chnical aspect of our work is the continuity of the matrix range of a cont
inuous field of operators\, and a certain quantitative matrix valued Hahn-
Babach type separation theorem. \nBased on joint work with Malte Gerhold.
\n\n Export\n \n\n \nsubscribe iCal
DTSTART;TZID=Asia/Jerusalem:20191204T120000
DTEND;TZID=Asia/Jerusalem:20191204T130000
LAST-MODIFIED:20191121T050055Z
SUMMARY:Analysis Seminar: Orr Shalit (Technion) ' On the matrix range of ra
ndom matrices'
URL;TYPE=URI:https://mathematics.huji.ac.il/event/analysis-seminar-orr-shal
it-technion-tba
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