The distance from a point to a cone in a Hilbert space.

Khudalov, V.T.

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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.

The facial structure of the finite dimensional latticial cone.

Németh, A.B. (2004)

Mathematica Pannonica

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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,...

On quasipositive elements in ordered Banach algebras

Gerd Herzog, Roland Lemmert (1998)

Studia Mathematica

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Let a real Banach algebra A with unit be ordered by an algebra cone K. We study the elements a ∈ A with exp(ta) ∈ K, t≥ 0.

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.

Applications of the scarcity theorem in ordered Banach algebras

Sonja Mouton (2014)

Studia Mathematica

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We apply Aupetit's scarcity theorem to obtain stronger versions of many spectral-theoretical results in ordered Banach algebras in which the algebra cone has generating properties.

Small operators between Banach and Hilbert spaces

R. Dudley (1970)

Studia Mathematica

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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...

Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces

Luděk Zajíček (1991)

Czechoslovak Mathematical Journal

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On self-conjugate Banach spaces

R. Sztencel, P. Zaremba (1981)

Colloquium Mathematicae

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The base-normed space of a unital group

Thurlow A. Cook, David J. Foulis (2004)

Mathematica Slovaca

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