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A lifting theorem for locally convex subspaces of L 0

R. Faber (1995)

Studia Mathematica

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 .

An additivity formula for the strict global dimension of C(Ω)

Seytek Tabaldyev (2014)

Open Mathematics

Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .

Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras

Amir Sahami, Mohammad R. Omidi, Eghbal Ghaderi, Hamzeh Zangeneh (2020)

Commentationes Mathematicae Universitatis Carolinae

We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space X , the Lipschitz algebras Lip α ( X ) and lip α ( X ) are approximately biflat if and only if X is finite, provided that 0 < α < 1 . We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.

Banach spaces

Laurent Gruson, Marius van der Put (1974)

Mémoires de la Société Mathématique de France

Bounded linear maps between (LF)-spaces.

Angela A. Albanese (2003)


Characterizations of pairs (E,F) of complete (LF)?spaces such that every continuous linear map from E to F maps a 0?neighbourhood of E into a bounded subset of F are given. The case of sequence (LF)?spaces is also considered. These results are similar to the ones due to D. Vogt in the case E and F are Fréchet spaces. The research continues work of J. Bonet, A. Galbis, S. Önal, T. Terzioglu and D. Vogt.

Extensions of certain real rank zero C * -algebras

Marius Dadarlat, Terry A. Loring (1994)

Annales de l'institut Fourier

G. Elliott extended the classification theory of A F -algebras to certain real rank zero inductive limits of subhomogeneous C * -algebras with one dimensional spectrum. We show that this class of C * -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the K 1 -group. Perturbation and lifting results are provided for certain subhomogeneous C * -algebras.

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