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Acknowledgement of priority: Separable quotients of Banach spaces.

Marek Wójtowicz (1998)

Collectanea Mathematica

In previous papers, it is proved, among other things, that every infinite dimensional sigma-Dedekind complete Banach lattice has a separable quotient. It has come to my attention that L. Weis proved this result without assuming sigma-Dedekind completeness; the proof is based, however, on the deep theorem of J. Hagler and W.B. Johnson concerning the structure of dual balls of Banach spaces and therefore cannot be applied simply to the case of locally convex solid topologically complete Riesz spaces....

Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries

An De Rijdt, Nikolas Vander Vennet (2010)

Annales de l’institut Fourier

The notion of monoidal equivalence for compact quantum groups was recently introduced by Bichon, De Rijdt and Vaes. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital C * -algebras or on von Neumann algebras. This correspondence turns out to be very useful to obtain the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups. Finally, we apply these results to identify the Poisson boundary...

Acyclic inductive spectra of Fréchet spaces

Jochen Wengenroth (1996)

Studia Mathematica

We provide new characterizations of acyclic inductive spectra of Fréchet spaces which improve the classical theorem of Palamodov and Retakh. It turns out that acyclicity, sequential retractivity (defined by Floret) and further strong regularity conditions (introduced e.g. by Bierstedt and Meise) are all equivalent. This solves a problem that was folklore since around 1970. For inductive limits of Fréchet-Montel spaces we obtain even stronger results, in particular, Grothendieck's problem whether...

Adaptive Deterministic Dyadic Grids on Spaces of Homogeneous Type

Richard Lechner, Markus Passenbrunner (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.

Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)

Aydin Sh. Shukurov (2014)

Colloquium Mathematicae

It is well known that if φ(t) ≡ t, then the system φ ⁿ ( t ) n = 0 ∞ is not a Schauder basis in L₂[0,1]. It is natural to ask whether there is a function φ for which the power system φ ⁿ ( t ) n = 0 ∞ is a basis in some Lebesgue space L p . The aim of this short note is to show that the answer to this question is negative.

Addendum to: "Sequences of 0's and 1's" (Studia Math. 149 (2002), 75-99)

Johann Boos, Toivo Leiger (2005)

Studia Mathematica

There is a nontrivial gap in the proof of Theorem 5.2 of [2] which is one of the main results of that paper and has been applied three times (cf. [2, Theorem 5.3, (G) in Section 6, Theorem 6.4]). Till now neither the gap has been closed nor a counterexample found. The aim of this paper is to give, by means of some general results, a better understanding of the gap. The proofs that the applications hold will be given elsewhere.

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