The -weak compactness of weak Banach-Saks operators
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
The Banach fixed point method for Ito stochastic differential equations
The Banach space c0.
The Banach space H...(X, d, ...).I.
The Banach space H...(X, d, ...).II.
The Banach space S is complementably minimal and subsequentially prime
We first include a result of the second author showing that the Banach space S is complementably minimal. We then show that every block sequence of the unit vector basis of S has a subsequence which spans a space isomorphic to its square. By the Pełczyński decomposition method it follows that every basic sequence in S which spans a space complemented in S has a subsequence which spans a space isomorphic to S (i.e. S is a subsequentially prime space).
The Banach Spaces ...p(n) for large p and n.
The Banach-Saks property and Haar null sets
A characterization of Haar null sets in the sense of Christensen is given. Using it, we show that if the dual of a Banach space has the Banach-Saks property, then closed and convex subsets of with empty interior are Haar null.
The Banach-Saks property in rearrangement invariant spaces
This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the...
The band generated by homomorphisms on Banach lattices.
This paper will consider the closure of the set of operators which may be expressed as a sum of lattice homomorphisms whose range is contained in a Dedekind complete Banch lattice.
The base-normed space of a unital group
The basis properties of power systems in .
The Bessaga-Pelczynski Property and Strongly Bounded Measures
The best constants in the Khintchine inequality
The bidual of a tensor product of Banach spaces.
This paper studies the relationship between the bidual of the (projective) tensor product of Banach spaces and the tensor product of their biduals.
The bidual of the space of polynomials on a Banach space.
The Bishop-Phelps-Bollobás property for numerical radius in ℓ₁(ℂ)
We show that the set of bounded linear operators from X to X admits a Bishop-Phelps-Bollobás type theorem for numerical radius whenever X is ℓ₁(ℂ) or c₀(ℂ). As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for ℓ₁(ℂ).
The bottleneck conjecture.
The bounded approximation property for the predual of the space of bounded holomorphic mappings
When U is the open unit ball of a separable Banach space E, we show that , the predual of the space of bounded holomorphic mappings on U, has the bounded approximation property if and only if E has the bounded approximation property.
The bounded approximation property for weakly uniformly continuous type holomorphic mappings.