Displaying similar documents to “The distance from a point to a cone in a Hilbert space.”

Domination properties in ordered Banach algebras

H. du T. Mouton, S. Mouton (2002)

Studia Mathematica

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We recall from [9] the definition and properties of an algebra cone C of a real or complex Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A. The Banach algebra A is then called an ordered Banach algebra. An important property that the algebra cone C may have is that of normality. If C is normal, then the order structure and the topology of A are reconciled in a certain way. Ordered Banach algebras have interesting...

An intermediate value theorem in ordered Banach spaces

Gerd Herzog (2010)

Annales Polonici Mathematici

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We prove an intermediate value theorem for certain quasimonotone increasing functions in ordered Banach spaces, under the assumption that each nonempty order bounded chain has a supremum.

Applications of nonnegative operators to a class of optimization problems

K. C. Sivakumar (2008)

Banach Center Publications

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Let X be a partially ordered real Banach space, a,b ∈ X with a ≤ b. Let ϕ be a bounded linear functional on X. We call X a Ben-Israel-Charnes space (or a B-C space) if the linear program defined by Maximize ϕ(x) subject to a ≤ x ≤ b has an optimal solution for any ϕ, a and b. Such problems arise naturally in solving a class of problems known as Interval Linear Programs. B-C spaces were introduced in the author's doctoral thesis and were subsequently studied in [8] and [9]. In this article,...

Special symmetries of Banach spaces isomorphic to Hilbert spaces

Jarno Talponen (2010)

Studia Mathematica

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We characterize Hilbert spaces among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.

Ordered analytic Hilbert spaces over the unit disk

Shengzhao Hou, Shuyun Wei (2008)

Studia Mathematica

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Let f, g be in the analytic function ring Hol(𝔻) over the unit disk 𝔻. We say that f ⪯ g if there exist M > 0 and 0 < r < 1 such that |f(z)| ≤ M|g(z)| whenever r < |z| < 1. Let X be a Hilbert space contained in Hol(𝔻). Then X is called an ordered Hilbert space if f ⪯ g and g ∈ X imply f ∈ X. In this note, we mainly study the connection between an ordered analytic Hilbert space and its reproducing kernel. We also consider when an invariant subspace of the whole space...