Abstract view
Representation of Banach Ideal Spaces and Factorization of Operators


Published:20051001
Printed: Oct 2005
Evgenii I. Berezhnoĭ
Lech Maligranda
Abstract
Representation theorems are proved for Banach ideal spaces with the Fatou property
which are built by the Calder{\'o}nLozanovski\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}nLozanovski\u\i\ construction
are involved in the proofs.
Keywords: 
Banach ideal spaces, weighted spaces, weight functions, CalderónLozanovski\u\i\ spaces, Orlicz spaces, representation of, spaces, uniqueness problem, positive linear operators, positive sublinear, operators, Schur test, factorization of operators, f
Banach ideal spaces, weighted spaces, weight functions, CalderónLozanovski\u\i\ spaces, Orlicz spaces, representation of, spaces, uniqueness problem, positive linear operators, positive sublinear, operators, Schur test, factorization of operators, f

MSC Classifications: 
46E30, 46B42, 46B70 show english descriptions
Spaces of measurable functions ($L^p$spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Banach lattices [See also 46A40, 46B40] Interpolation between normed linear spaces [See also 46M35]
46E30  Spaces of measurable functions ($L^p$spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46B42  Banach lattices [See also 46A40, 46B40] 46B70  Interpolation between normed linear spaces [See also 46M35]
