A Characterization of Weakly Sequentially Complete Banach Lattices.
A characterization of weakly sequentially complete Banach lattices
The equivalence of the two following properties is proved for every Banach lattice :1) is weakly sequentially complete.2) Every -Borel measurable linear functional on is -continuous.
A C(K) Banach space which does not have the Schroeder-Bernstein property
We construct a totally disconnected compact Hausdorff space K₊ which has clopen subsets K₊” ⊆ K₊’ ⊆ K₊ such that K₊” is homeomorphic to K₊ and hence C(K₊”) is isometric as a Banach space to C(K₊) but C(K₊’) is not isomorphic to C(K₊). This gives two nonisomorphic Banach spaces (necessarily nonseparable) of the form C(K) which are isomorphic to complemented subspaces of each other (even in the above strong isometric sense), providing a solution to the Schroeder-Bernstein problem for Banach spaces...
A class of Banach lattices and positive operators
A class of Banach sequence spaces analogous to the space of Popov
Hagler and the first named author introduced a class of hereditarily Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily Banach spaces for . Here we use these spaces to introduce a new class of hereditarily Banach spaces analogous of the space of Popov. In particular, for the spaces are further examples of hereditarily Banach spaces failing the Schur property.
A class of -preduals which are isomorphic to quotients of
For every countable ordinal α, we construct an -predual which is isometric to a subspace of and isomorphic to a quotient of . However, is not isomorphic to a subspace of .
A class of operators from a Banach lattice into a Banach space.
A class of precompact sets in Banach spaces.
A class of spaces lacking normal structure
A classification of separable Rosenthal compacta and its applications [Book]
A coding of separable Banach spaces. Analytic and coanalytic families of Banach spaces
When the set of closed subspaces of C(Δ), where Δ is the Cantor set, is equipped with the standard Effros-Borel structure, the graph of the basic relations between Banach spaces (isomorphism, being isomorphic to a subspace, quotient, direct sum,...) is analytic non-Borel. Many natural families of Banach spaces (such as reflexive spaces, spaces not containing ℓ₁(ω),...) are coanalytic non-Borel. Some natural ranks (rank of embedding, Szlenk indices) are shown to be coanalytic ranks. Applications...
A coefficient related to some geometric properties of a Banach space.
A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings
It is shown that if 𝓢 is a commuting family of weak* continuous nonexpansive mappings acting on a weak* compact convex subset C of the dual Banach space E, then the set of common fixed points of 𝓢 is a nonempty nonexpansive retract of C. This partially solves an open problem in metric fixed point theory in the case of commutative semigroups.
A Compact Operator Characterization of l1.
A compactness criterion of mixed Krasnoselskiĭ-Riesz type in regular ideal spaces of vector functions.
A comparative analysis of Bernstein type estimates for the derivative of multivariate polynomials
We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed ellipse method...
A complement of positive weak almost Dunford-Pettis operators on Banach lattices
In this paper, we give some necessary and sufficient conditions such that each positive operator between two Banach lattices is weak almost Dunford-Pettis, and we derive some interesting results about the weak Dunford-Pettis property in Banach lattices.
A conditional quasi-greedy basis of l₁
We show that the Lindenstrauss basic sequence in l₁ may be used to construct a conditional quasi-greedy basis of l₁, thus answering a question of Wojtaszczyk. We further show that the sequence of coefficient functionals for this basis is not quasi-greedy.
A conjecture about the Dunford-Pettis property
A construction of a base for the m fold tensor product of a Banach space.