### 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 $\u27e8{\u27e9}_{\phi}$ (see [26]) and its Gagliardo closure on couples of...

### A Characterization of Totally Reflexive Fréchet Spaces.

### A Class of C*-algebras and Topological Markov Chains II: Reducible Chains and the Ext-functor for C*-algebras.

### A class of locally convex spaces without $\mathcal{C}$-webs

In this article we give some properties of the tensor product, with the $\u03f5$ and $\pi $ topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.

### A Coifman-Rochberg type characterization of quasi-power weights.

### A commutator theorem with applications.

We give an extension of the commutator theorems of Jawerth, Rochberg and Weiss [9] for the real method of interpolation. The results are motivated by recent work by Iwaniek and Sbordone [6] on generalized Hodge decompositions. The main estimates of these authors are based on a commutator theorem for a specific operator acting on Lp spaces and through the use of the complex method of interpolation. In this note we give an extension of the Iwaniek-Sbordone theorem to general real interpolation scales....

### A construction of a base for the m fold tensor product of a Banach space.

### A construction of simplicial objects

We construct a simplicial locally convex algebra, whose weak dual is the standard cosimplicial topological space. The construction is carried out in a purely categorical way, so that it can be used to construct (co)simplicial objects in a variety of categories --- in particular, the standard cosimplicial topological space can be produced.

### A direct sum is holomorphically bornological with the topology induced by a cartesian product

### A Duality Theorem for Locally Convex Tensor Products.

### A family of Kučera spaces

### A Free Convenient Vector Space for Holomorphic Spaces.

### A function parameter in connection with interpolation of Banach spaces.

### A generalization of the Shimogaki theorem

### A Lifting Result for Locally Pseudo-Convex Subspaces of L₀

It is shown that if F is a topological vector space containing a complete, locally pseudo-convex subspace E such that F/E = L₀ then E is complemented in F and so F = E⊕ L₀. This generalizes results by Kalton and Peck and Faber.

### A lifting theorem for locally convex subspaces of ${L}_{0}$

We prove that for every closed locally convex subspace E of ${L}_{0}$ and for any continuous linear operator T from ${L}_{0}$ to ${L}_{0}/E$ there is a continuous linear operator S from ${L}_{0}$ to ${L}_{0}$ such that T = QS where Q is the quotient map from ${L}_{0}$ to ${L}_{0}/E$.

### A local version of the Dauns-Hofmann theorem.

### A multidimensional Wolff theorem

### A multilinear interpolation theorem