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1. CJM 2007 (vol 59 pp. 614)
Preduals and Nuclear Operators Associated with Bounded, $p$-Convex, $p$-Concave and Positive $p$-Summing Operators |
Preduals and Nuclear Operators Associated with Bounded, $p$-Convex, $p$-Concave and Positive $p$-Summing Operators We use Krivine's form of the Grothendieck inequality
to renorm the space of bounded linear maps acting between Banach
lattices. We
construct preduals and describe the nuclear operators
associated with these preduals for this renormed space
of bounded operators as well as for
the spaces of $p$-convex,
$p$-concave and positive $p$-summing operators acting
between Banach lattices and Banach spaces.
The nuclear operators obtained are described in
terms of factorizations through
classical Banach spaces via positive operators.
Keywords:$p$-convex operator, $p$-concave operator, $p$-summing operator, Banach space, Banach lattice, nuclear operator, sequence space Categories:46B28, 47B10, 46B42, 46B45 |
2. CJM 1999 (vol 51 pp. 309)
Symmetric sequence subspaces of $C(\alpha)$, II If $\alpha$ is an ordinal, then the space of all ordinals less than or
equal to $\alpha$ is a compact Hausdorff space when endowed with the
order topology. Let $C(\alpha)$ be the space of all continuous
real-valued functions defined on the ordinal interval $[0,
\alpha]$. We characterize the symmetric sequence spaces which embed
into $C(\alpha)$ for some countable ordinal $\alpha$. A hierarchy
$(E_\alpha)$ of symmetric sequence spaces is constructed so that, for
each countable ordinal $\alpha$, $E_\alpha$ embeds into
$C(\omega^{\omega^\alpha})$, but does not embed into
$C(\omega^{\omega^\beta})$ for any $\beta < \alpha$.
Categories:03E13, 03E15, 46B03, 46B45, 46E15, 54G12 |
3. CJM 1997 (vol 49 pp. 1242)
$1$-complemented subspaces of spaces with $1$-unconditional bases We prove that if $X$ is a complex strictly monotone sequence
space with $1$-un\-con\-di\-tion\-al basis, $Y \subseteq X$ has no bands
isometric to $\ell_2^2$ and $Y$ is the range of norm-one projection from
$X$, then $Y$ is a closed linear span a family of mutually
disjoint vectors in $X$.
We completely characterize $1$-complemented subspaces and norm-one
projections in complex spaces $\ell_p(\ell_q)$ for $1 \leq p, q <
\infty$.
Finally we give a full description of the subspaces that are spanned
by a family of disjointly supported vectors and which are
$1$-complemented in (real or complex) Orlicz or Lorentz sequence
spaces. In particular if an Orlicz or
Lorentz space $X$ is not isomorphic to $\ell_p$ for some $1 \leq p <
\infty$ then the only subspaces
of $X$ which are $1$-complemented and disjointly supported are the
closed linear spans of block bases with constant
coefficients.
Categories:46B20, 46B45, 41A65 |