A Class of Bornological Barrelled Spaces which Are not Ultrabornological.
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...
A positive operator A and a closed subspace of a Hilbert space ℋ are called compatible if there exists a projector Q onto such that AQ = Q*A. Compatibility is shown to depend on the existence of certain decompositions of ℋ and the ranges of A and . It also depends on a certain angle between A() and the orthogonal of .