A note on the modulus of -convexity and modulus of -convexity.
A note on the paper of Shütt "Unconditionality in tensor products''
A note on the predual of Lip(S, d)
A note on the structure of WUR Banach spaces
We present an example of a Banach space admitting an equivalent weakly uniformly rotund norm and such that there is no , for any set , linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space is actually the dual space of a space which is a subspace of a WCG space.
A note on Tsirelson type ideals
Using Tsirelson’s well-known example of a Banach space which does not contain a copy of or , for p ≥ 1, we construct a simple Borel ideal such that the Borel cardinalities of the quotient spaces and are incomparable, where is the summable ideal of all sets A ⊆ ℕ such that . This disproves a “trichotomy” conjecture for Borel ideals proposed by Kechris and Mazur.
A note on weakly Lindelöf determined Banach spaces
We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given.
A notion of Orlicz spaces for vector valued functions
The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on -functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of , and representations of the dual space.
A Perron FrobeniusTheory for Representations of Locally Compact Abelian Groups.
A probabilistic version of the Frequent Hypercyclicity Criterion
For a bounded operator T on a separable infinite-dimensional Banach space X, we give a "random" criterion not involving ergodic theory which implies that T is frequently hypercyclic: there exists a vector x such that for every non-empty open subset U of X, the set of integers n such that Tⁿx belongs to U, has positive lower density. This gives a connection between two different methods for obtaining the frequent hypercyclicity of operators.
A Prokhorov's theorem for Banach lattice valued measures.
A proof of admissibility of a class of random normed spaces
A proof of the Grünbaum conjecture
Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N ∈ N with N ≥ n define , λₙ = supλ(V): dim(V) = n. A well-known Grünbaum conjecture [Trans. Amer. Math. Soc. 95 (1960)] says that λ₂ = 4/3. König and Tomczak-Jaegermann [J. Funct. Anal. 119 (1994)] made an attempt to prove this conjecture. Unfortunately, their Proposition 3.1, used in the proof, is incorrect. In this paper a complete proof of the Grünbaum conjecture is presented
A proof of the Huff-Morris Radon-Nikodym theorem
A property of quasi-complements
A Pythagorean approach in Banach spaces.
A quantitative version of Krein's theorem.
A quantitative version of Krein's Theorem on convex hulls of weak compact sets is proved. Some applications to weakly compactly generated Banach spaces are given.
A quasi-dichotomy for C(α,X) spaces, α < ω₁
We prove the following quasi-dichotomy involving the Banach spaces C(α,X) of all X-valued continuous functions defined on the interval [0,α] of ordinals and endowed with the supremum norm. Suppose that X and Y are arbitrary Banach spaces of finite cotype. Then at least one of the following statements is true. (1) There exists a finite ordinal n such that either C(n,X) contains a copy of Y, or C(n,Y) contains a copy of X. (2) For any infinite countable...
A reflexive Banach space which is not sufficiently Euclidean
A Relation between Diagonal and Unconditional Basis Constants.
A remark on -spaces.