Disjointly strictly singular operators and interpolation (original) (raw)
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Strictly singular and power-compact operators on Banach lattices
preprint
Compactness of the iterates of strictly singular operators on Banach lattices is analyzed. We provide suitable conditions on the behavior of disjoint sequences in a Banach lattice, for strictly singular operators to be Dunford-Pettis, compact or have compact square. Special emphasis is given to the class of rearrangement invariant function spaces (in particular, Orlicz and Lorentz spaces). Moreover, examples of rearrangement invariant function spaces of xed arbitrary indices with strictly singular non power-compact operators are also presented.
Memoirs of the American Mathematical Society, 2003
Interpolation of Weighted Banach Lattices It is Interpolation of weighted Banach lattices : A characterization .-Trove (Memoirs of the American Mathematical Society; 1193). Interpolation of weighted Banach lattices, a characterization of relatively decomposable Banach Symmetrization, factorization and arithmetic of quasi-Banach. A characterization of relatively decomposable Banach lattices Two Banach lattices of. Article in Memoirs of the American Mathematical Society 787(787) Interpolation Of Weighted Banach Lattices-Gloria Gone Traveling. 17 Jan 2018. arXiv:1801.05799v1 [math. We investigate relations between symmetrizations of quasi-Banach function. The weighted quasi-normed ideal space E(w), where w: I ? (0, .. 93] and ?(E,F) is an interpolation space between E and A characterization of relatively decomposable Banach lattices, Mem. Interpolation of weighted Banach lattices. A characterization of SERIES: Memoirs of the American Mathematical Society, no. 784 TITLE: Interpolation of weighted Banach lattices ; A characterization of relatively decomposable Banach lattices / Michael Cwikel, Per G. Nilsson, Gideon Schechtman. Interpolation of Weighted Banach Lattices: A Characterization of. Online American Mathematical Society Journals-from 1950 volume: 1 issue: 1. Interpolation of weighted Banach lattices ; A characterization of relatively Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines / Hagen Meltzer. Memoirs of the American Mathematical Society, no. Interpolation of weighted Banach lattices Michael Cwikel, Per G. Request PDF on ResearchGate Interpolation of weighted Banach lattices It is. of Banach spaces (A0, A1) it is possible to characterize all interpolation spaces with Article in Memoirs of the American Mathematical Society 165(787):1-105 all relative interpolation spaces with respect to the weighted couples (X 0,w0, Interpolation of Weighted Banach Lattices/A Characterization of .
Disjointly non-singular operators on Banach lattices
Journal of Functional Analysis, 2021
An operator T from a Banach lattice E into a Banach space is disjointly non-singular (DN-S, for short) if no restriction of T to a subspace generated by a disjoint sequence is strictly singular. We obtain several results for DN-S operators, including a perturbative characterization. For E = L p (1 < p < ∞) we improve the results, and we show that the DN-S operators have a different behavior in the cases p = 2 and p = 2. As an application we prove that the strongly embedded subspaces of L p form an open subset in the set of all closed subspaces.
c 0-Singular and ℓ 1-singular operators between vector-valued Banach lattices
Positivity
Given an operator T : X --> Y between Banach spaces, and a Banach lattice E consisting of measurable functions, we consider the point-wise extension of the operator to the vector-valued Banach lattices TE : E(X) --> E(Y ) given by TE(f)(x) = T(f(x)). It is proved that for any Banach lattice E which does not contain c0, the operator T is an isomorphism on a subspace isomorphic to c0 if and only if so is TE. An analogous result for invertible operators on subspaces isomorphic to l1 is also given.
Characterizations of strictly singular operators on Banach lattices
Journal of the London …, 2009
New characterizations of strictly singular operators between Banach lattices are given. It is proved that for Banach lattices X and Y , such that X has fi nite cotype and Y satis es a lower 2-estimate, an operator T : X -->Y is strictly singular if and only if it is disjointly strictly singular and l2-singular. Moreover, if T is regular the same equivalence holds provided Y is just order continuous. Furthermore, it is shown that these results fail if the conditions on the lattices are relaxed.
SOME PROPERTIES OF STRICTLY SINGULAR OPERATORS ON BANACH LATTICES
maia.ub.es
Several results obtained during the author's Ph.D. Thesis are presented. In particular, domination results (in Dodds-Fremlin sense) for the ideal of strictly singular operators will be given. Moreover, the connections between strictly singular and the classes of AM-compact, l2-singular and disjointly strictly singular are studied. As an application we obtain existence of invariant subspaces for positive strictly singular operators. On a di erent direction, results on compact powers of strictly singular operators are also presented extending a theorem of V. Milman. Finally, we study when a c0-singular or l1-singular operator can be extended to an operator between vector valued lattices preserving its singularity properties.
Riesz spaces of order bounded disjointness preserving operators
2007
Let L, M be Archimedean Riesz spaces and Lb(L, M) be the ordered vector space of all order bounded operators from L into M . We define a Lamperti Riesz subspace of Lb(L, M) to be an ordered vector subspace L of Lb(L, M) such that the elements of L preserve disjointness and any pair of operators in L has a supremum in Lb(L, M) that belongs to L. It turns out that the lattice operations in any Lamperti Riesz subspace L of Lb(L, M) are given pointwise, which leads to a generalization of the classic Radon-Nikodým theorem for Riesz homomorphisms. We then introduce the notion of maximal Lamperti Riesz subspace of Lb(L, M) as a generalization of orthomorphisms. In this regard, we show that any maximal Lamperti Riesz subspace of Lb(L, M) is a band of Lb(L, M), provided M is Dedekind complete. Also, we extend standard transferability theorems for orthomorphisms to maximal Lamperti Riesz subspace of Lb(L, M). Moreover, we give a complete description of maximal Lamperti Riesz subspaces on some...
A quantitative approach to disjointly non-singular operators
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021
We introduce and study some operational quantities which characterize the disjointly non-singular operators from a Banach lattice E to a Banach space Y when E is order continuous, and some other quantities which characterize the disjointly strictly singular operators for arbitrary E.
l∞ AND INTERPOLATION BETWEEN BANACH LATTICES
1997
We study the possibility of obtaining the l∞-norm by an interpolation method starting from a couple of Banach lattice norms. We describe all couples of Banach lattice norms in Rn such that the l∞-norm is a strict interpolation norm between them. Further we consider the possibility of obtaining the l∞-norm by any method which guarantees interpolation of not only linear operators ( = bilinear forms on Rn×Rn) but also of all polylinear forms. Here we show that either one of the initial norms has to be proportional to the l∞-norm, or both have to be weighted l∞-norms. Introduction The problem discussed in this article was inspired by a question posed by N. Kalton (Workshop on Interpolation spaces, Haifa, 1990), which he formulated as follows: is l∞ a black hole? He noticed that it is impossible to obtain the space l∞ by the complex method construction starting from a wide range of Banach couples both non-isometric to l∞ (including, in particular, couples of Banach lattices). He asked wh...
A unified approach to compatibility theorems on invertible interpolated operators
arXiv: Functional Analysis, 2020
We prove the stability of isomorphisms between Banach spaces generated by interpolation methods introduced by Cwikel-Kalton-Milman-Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also the so-called pm\pmpm or G_1G_1G1 and G2G_2G_2 methods defined by Peetre and Gustavsson-Peetre. This result is used to show the existence of solution of certain operator analytic equation. A by product of these results is a more general variant of the Albrecht-Muller result which states that the interpolated isomorphisms satisfy uniqueness-of-inverses between interpolation spaces. We show applications for positive operators between Calderon function lattices. We also derive connections between the spectrum of interpolated operators.