Expand all Collapse all | Results 1 - 4 of 4 |
1. CJM 2008 (vol 60 pp. 520)
Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences Let $A=(a_{j,k})_{j,k \ge 1}$ be a non-negative matrix. In this
paper, we characterize those $A$ for which $\|A\|_{E, F}$ are
determined by their actions on decreasing sequences, where $E$ and
$F$ are suitable normed Riesz spaces of sequences. In particular,
our results can apply to the following spaces: $\ell_p$, $d(w,p)$,
and $\ell_p(w)$. The results established here generalize
ones given by Bennett; Chen, Luor, and Ou; Jameson; and
Jameson and Lashkaripour.
Keywords:norms of matrices, normed Riesz spaces, weighted mean matrices, NÃ¶rlund mean matrices, summability matrices, matrices with row decreasing Categories:15A60, 40G05, 47A30, 47B37, 46B42 |
2. 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 |
3. CJM 2005 (vol 57 pp. 897)
Representation of Banach Ideal Spaces and Factorization of Operators Representation theorems are proved for Banach ideal spaces with the Fatou property
which are built by the Calder{\'o}n--Lozanovski\u\i\ construction.
Factorization theorems for operators in spaces more general than the Lebesgue
$L^{p}$ spaces are investigated. It is natural to extend the Gagliardo
theorem on the Schur test and the Rubio de~Francia theorem on factorization of the
Muckenhoupt $A_{p}$ weights to reflexive Orlicz spaces. However, it turns out that for
the scales far from $L^{p}$-spaces this is impossible. For the concrete integral operators
it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces
are not valid. Representation theorems for the Calder{\'o}n--Lozanovski\u\i\ construction
are involved in the proofs.
Keywords:Banach ideal spaces, weighted spaces, weight functions,, CalderÃ³n--Lozanovski\u\i\ spaces, Orlicz spaces, representation of, spaces, uniqueness problem, positive linear operators, positive sublinear, operators, Schur test, factorization of operators, f Categories:46E30, 46B42, 46B70 |
4. CJM 2000 (vol 52 pp. 789)
The Dunford-Pettis Property for Symmetric Spaces A complete description of symmetric spaces on a separable measure
space with the Dunford-Pettis property is given. It is shown that
$\ell^1$, $c_0$ and $\ell^{\infty}$ are the only symmetric sequence
spaces with the Dunford-Pettis property, and that in the class of
symmetric spaces on $(0, \alpha)$, $0 < \alpha \leq \infty$, the only
spaces with the Dunford-Pettis property are $L^1$, $L^{\infty}$, $L^1
\cap L^{\infty}$, $L^1 + L^{\infty}$, $(L^{\infty})^\circ$ and $(L^1 +
L^{\infty})^\circ$, where $X^\circ$ denotes the norm closure of $L^1
\cap L^{\infty}$ in $X$. It is also proved that all Banach dual
spaces of $L^1 \cap L^{\infty}$ and $L^1 + L^{\infty}$ have the
Dunford-Pettis property. New examples of Banach spaces showing that
the Dunford-Pettis property is not a three-space property are also
presented. As applications we obtain that the spaces $(L^1 +
L^{\infty})^\circ$ and $(L^{\infty})^\circ$ have a unique symmetric
structure, and we get a characterization of the Dunford-Pettis
property of some K\"othe-Bochner spaces.
Categories:46E30, 46B42 |