From: Brenda Cook (brenda@math.missouri.edu)
Date: Tue Nov 14 2006 - 11:50:02 CST
COLLOQUIUM
University of Missouri-Columbia
Department of Mathematics
Hermann Koenig
University of Kiel, Germany
On the problem of the best constant
in Grothendieck’s inequality
Grothendieck in his work on topological tensor products of Banach spaces
in the early 1950's proved an inequality which is fundamental in studying
unconditional and absolute convergence and unconditional bases in Banach
spaces. The inequality means that bounded linear operators from L_infinity
to L_1 may be tensorized with the identity on a Hilbert space, yielding a
bounded linear operator whose norm is increased at most by a fixed
constant. The best "Grothendieck-" constant is still unknown, and the
lecture will outline what is known. The constant for complex Banach spaces
is smaller than the one for real spaces. In the real case, the upper bound
of the Grothendieck constant by Krivine - Pi/(2*ln(1+sqrt(2)) - is
conjectured to be optimal.
3:30-4:20 p.m.
Tuesday, November 14
114 General Classroom Building
Refreshments will be served at 3:00 p.m. in Room 326 Mathematical
Sciences (Math Lounge).
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