We consider interpolation of unital Banach algebras, in the special case when the intersection space is non-unital, giving precise conditions of when an interpolation algebra is unital.

1. Iwasawa functions, p-adic measures, and distributions 1 1.1. Some preliminaries 1 1.2. Iwasawa functions and the Iwasawa algebra 3 1.3. Iwasawa functions and interpolation 4 1.4. p-adic distributions and p-adic measures 8 2. The p-adic L-functions of Dirichlet characters 10 2.1. Preliminaries 10 2.2. Iwasawa’s construction 12 3. The p-adic L-functions of modular forms 15 3.1. Preliminaries 1...

We describe the real interpolation spaces between given Marcinkiewicz spaces that have fundamental functions of the form t ( ln et )α with the same exponent q. The spaces thus obtained are used for the proof of optimal interpolation theorem from [7], concerning spaces L∞,α,E .

Article history: Received 13 February 2012 Received in revised form 24 August 2012 Accepted 25 September 2012 Available online 13 October 2012

It is shown that, for any field F ⊆ R, any ordered vector space structure of F with Riesz interpolation is given by an inductive limit of sequence with finite stages (F,F≥0) (where n does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with F replaced by the integers, Z. Indeed, it shows that although Effros and Shen’s ...

We introduce a wide class of tensor norms gλ,ρ which are defined with the help of interpolation spaces between perfect sequence spaces defined by a general parameter real interpolation method. We also characterize the associated λρ-nuclear and λρintegral operators.

Given a function f : E → R with E ⊂ Rn, we explain how to decide whether f extends to a Cm function F on Rn. If E is finite, then one can efficiently compute an F as above, whose Cm norm has the least possible order of magnitude (joint work with B. Klartag).