On the p-drop theorem, 1 ≤ p ≤∞.
Abdelhakim Maaden (2002)
Extracta Mathematicae
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Abdelhakim Maaden (2002)
Extracta Mathematicae
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C. J. Atkin (2001)
Studia Mathematica
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Let f be a smooth function defined on a finite union U of open convex sets in a locally convex Lindelöf space E. If, for every x ∈ U, the restriction of f to a suitable neighbourhood of x admits a smooth extension to the whole of E, then the restriction of f to a union of convex sets that is strictly smaller than U also admits a smooth extension to the whole of E.
Zajíček, L.
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S. Dierolf, P. Domański (1993)
Studia Mathematica
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Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given. ...
S. A. Shkarin (2006)
Studia Mathematica
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Herzog and Lemmert have proven that if E is a Fréchet space and T: E → E is a continuous linear operator, then solvability (in [0,1]) of the Cauchy problem ẋ = Tx, x(0) = x₀ for any x₀ ∈ E implies solvability of the problem ẋ(t) = Tx(t) + f(t,x(t)), x(0) = x₀ for any x₀ ∈ E and any continuous map f: [0,1] × E → E with relatively compact image. We prove the same theorem for a large class of locally convex spaces including: • DFS-spaces, i.e., strong duals of Fréchet-Schwartz...
Wiktor Szczyrba (1971)
Studia Mathematica
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A. L. Brown, H. L. Vasudeva
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The paper is concerned with the Fréchet differentiability and operator convexity of the operator functions on sets of self-adjoint operators on finite-dimensional inner product spaces which are associated with real-valued functions of one or two variables. In Part I it is shown that if a real-valued function is L times continuously differentiable then the associated operator functions are L times Fréchet differentiable with continuous Fréchet derivatives. It is shown that the operator...
Mieczysław Altman (1984)
Banach Center Publications
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Abdelhakim Maâden (1995)
Collectanea Mathematica
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Seán Dineen (1975)
Bulletin de la Société Mathématique de France
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