Meeting 172
On Wednesday, April 24th, 2024 at 10:15 AM (room 1016 and MSTeams)
Jakub Markowiak
gives the lecture:Criteria for strong unicity of best approximation in Banach spaces.
Meeting 173
On Wednesday, May 8th, 2024 at 10:15 AM (room 1016 and MSTeams)
Tomasz Kobos
gives the lecture:Real normed spaces with the maximal Banach-Mazur distance to the Euclidean space in dimensions two and three
Abstract. One of the classical consequences of the famous John ellipsoid theorem is the fact that the Banach-Mazur distance of the n-dimensional Euclidan space and arbitrary n-dimensional normed space is not greater than sqrt(n). Moreover, it is easy to see that this estimate is optimal, for example for the l_oo space of dimension n or l_1 space of dimension n. In dimensions n>=4 it is well-known that there are also other examples of spaces with the distance sqrt(n), which are not isometric to l_1 or l_oo. However, what happens in the case of dimensions two and three? In this talk we shall provide an answer to this question and additionally a stability result in the planar case.
Meeting 174
On Wednesday, May 15th, 2024 at 10:15 AM (room 1016 and MSTeams)
Barbara Lewandowska
gives the lecture:On the maximal absolute projection constant
Abstract: Let X be a Banach space and Y be its finite-dimensional subspace. Let P(X,Y) denote the set of all linear and continuous projections from X onto Y, recalling that an operator P is called a projection onto Y if P|_Y=Id_Y. We define the relative projection constant of Y and X by lambda(Y,X) :=inf {||P||: P\in P(X,Y)} and the absolute projection constant of Y by lambda(Y) :=sup{lambda(Y,X): Y\subset X}, and finally, the maximal absolute projection constant by lambda(m) :=sup {lambda(Y): dim(Y)=m }. In the talk, we briefly present recent work on the subject and make conjectures based on some new concepts.
Meeting 175
On Wednesday, May 22nd, 2024 at 10:15 AM (room 1016 and MSTeams)
(to be announced)
gives the lecture:(to be announced)
Meeting 176
On Wednesday, May 29th, 2024 at 10:15 AM (room 1016 and MSTeams)
(to be announced)
gives the lecture:(to be announced)
Meeting 177
On Wednesday, June 5th, 2024 at 10:15 AM (room 1016 and MSTeams)
(to be announced)
gives the lecture:(to be announced)
Meeting 178
On Wednesday, June 12th, 2024 at 10:15 AM (room 1016 and MSTeams)
(to be announced)
gives the lecture:(to be announced)
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