A -algebra without generalized topological divisors of zero
A Banach principle for semifinite von Neumann algebras.
A Banach space determined by the Weil height
A Banach space dichotomy theorem for quotients of subspaces
A Banach space X with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable property if X/Y is hereditarily indecomposable for any infinite-codimensional subspace Y with a successive finite-dimensional decomposition on the basis of X. The following dichotomy theorem is proved: any infinite-dimensional Banach space contains a quotient of a subspace which either has an unconditional basis, or has the restricted quotient hereditarily indecomposable property.
A Banach space that is MLUR but not HR.
A Banach space with a symmetric basis which contains no or , and all its symmetric basic sequences are equivalent
A Banach space with a symmetric basis which is of weak cotype 2 but not of cotype 2
We prove that the symmetric convexified Tsirelson space is of weak cotype 2 but not of cotype 2.
A Bator's question on dual Banach spaces.
A Best Covering Problem.
A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces
We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ C(X) is equivalent to the uncountability of X. This is derived from a bilinear version of Holsztyński's theorem [3] on isometries of C(X)-spaces, which is also proved in the paper.
A bipolar theorem for L
A Borel extension approach to weakly compact operators on
Let be a quasicomplete locally convex Hausdorff space. Let be a locally compact Hausdorff space and let , is continuous and vanishes at infinity be endowed with the supremum norm. Starting with the Borel extension theorem for -valued -additive Baire measures on , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map to be weakly compact.
A bornological approach to rotundity and smoothness applied to approximation.
A -algebra on Schur algebras.
A -algebraic Schoenberg theorem
Let be a -algebra, a compact abelian group, an action of by -automorphisms of the fixed point algebra of and the dense sub-algebra of -finite elements in . Further let be a linear operator from into which commutes with and vanishes on . We prove that is a complete dissipation if and only if is closable and its closure generates a -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative definite...
A -dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking
In this paper we extend to arbitrary number fields a construction of Bost-Connes of a -dynamical system with spontaneous symmetry breaking and partition function the Riemann zeta function.
A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.
We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e.g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions.
A Carlson type inequality with blocks and interpolation
An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of “blocks” and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre’s interpolation functor (see [26]) and its Gagliardo closure on couples of...
A certain subspace of characteristic zero of
A chain rule formula for the composition of a vector-valued function by a piecewise smooth function
We state and prove a chain rule formula for the composition of a vector-valued function by a globally Lipschitz-continuous, piecewise function . We also prove that the map is continuous from into for the strong topologies of these spaces.