A class of Banach lattices and positive operators
Hagler and the first named author introduced a class of hereditarily Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily Banach spaces for . Here we use these spaces to introduce a new class of hereditarily Banach spaces analogous of the space of Popov. In particular, for the spaces are further examples of hereditarily Banach spaces failing the Schur property.
For every countable ordinal α, we construct an -predual which is isometric to a subspace of and isomorphic to a quotient of . However, is not isomorphic to a subspace of .
In this article we give some properties of the tensor product, with the and 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.
In [5] and [10], statistical-conservative and -conservative matrices were characterized. In this note we have determined a class of statistical and -conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem.
For an increasing sequence (ωₙ) of algebra weights on ℝ⁺ we study various properties of the Fréchet algebra A(ω) = ⋂ ₙ L¹(ωₙ) obtained as the intersection of the weighted Banach algebras L¹(ωₙ). We show that every endomorphism of A(ω) is standard, if for all n ∈ ℕ there exists m ∈ ℕ such that as t → ∞. Moreover, we characterise the continuous derivations on this algebra: Let M(ωₙ) be the corresponding weighted measure algebras and let B(ω) = ⋂ ₙM(ωₙ). If for all n ∈ ℕ there exists m ∈ ℕ such that...
La presente Nota contiene una lista di -algebre reali di dimensione finita ed una lista di -algebre complesse di dimensione finita tali che: 1) due elementi distinti di ogni lista non sono mai -isomorfi; 2) ogni -algebra di dimensione finita reale (complessa) è —isomorfa su (su ) alla somma diretta, finita, di -algebre reali (complesse) elencate nella lista. In altre parole, diamo qui una classificazione completa delle —algebre reali e delle -algebre complesse di dimensione finita. Nel...