Miguel Martin
On the numerical index of real $L_p(\mu)$-spaces.
Mon, 02/01/2010 - 16:01 — SomNambulAuthors: Miguel Martin, Javier Meri, Mikhail Popov
Subjects: Functional Analysis
AbstractWe give a lower bound for the numerical index of the real space $L_p(\mu)$
showing, in particular, that it is non-zero for $p\neq 2$. In other words, it
is shown that for every bounded linear operator $T$ on the real space
$L_p(\mu)$, one has $$ \sup{\Bigl|\int |x|^{p-1}\sign(x) T x d\mu \Bigr| : x\in
L_p(\mu), \|x\|=1} \geq \frac{M_p}{12\e}\|T\| $$ where
$M_p=\max_{t\in[0,1]}\frac{|t^{p-1}-t|}{1+t^p}>0$ for every $p\neq 2$.Isometries on extremely non-complex Banach spaces.
Mon, 02/01/2010 - 16:01 — SomNambulAuthors: Miguel Martin, Piotr Koszmider, Javier Meri
Subjects: Functional Analysis
AbstractGiven a separable Banach space $E$, we construct an extremely non-complex
Banach space (i.e. a space satisfying that $\|Id + T^2\|=1+\|T^2\|$ for every
bounded linear operator $T$ on it) whose dual contains $E^*$ as an $L$-summand.
We also study surjective isometries on extremely non-complex Banach spaces and
construct an example of a real Banach space whose group of surjective
isometries reduces to $\pm Id$, but the group of surjective isometries of its
dual contains the group of isometries of a separable infinite-dimensional
Hilbert space as a subgroup.On remotality for convex sets in Banach spaces.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Miguel Martin, T.S.S.R.K. Rao
Subjects: Functional Analysis
AbstractWe show that every infinite dimensional Banach space has a closed and bounded
convex set that is not remotal.
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