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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.
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.
Khudalov, V.T. (1999)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Gerd Herzog, Peer C. Kunstmann (2023)
Commentationes Mathematicae Universitatis Carolinae
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In ordered Banach algebras, we introduce eventually and asymptotically positive elements. We give conditions for the following spectral properties: the spectral radius belongs to the spectrum (Perron--Frobenius property); the spectral radius is the only element in the peripheral spectrum; there are positive (approximate) eigenvectors for the spectral radius. Recently such types of results have been shown for operators on Banach lattices. Our results can be viewed as a complement, since...
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,...
Burke, Maxim R., Wiesaw, Kubis, Stevo, Todorcevic (2006)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35. We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing...
J. R. Holub (1971)
Colloquium Mathematicae
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Stanisław Szufla (1977)
Annales Polonici Mathematici
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Jochen Reinermann (1970)
Annales Polonici Mathematici
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K. Goebel, E. Złotkiewicz (1971)
Colloquium Mathematicae
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Gerd Herzog, Christoph Schmoeger (2010)
Studia Mathematica
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We study boundary value problems of the type Ax = r, φ(x) = φ(b) (φ ∈ M ⊆ E*) in ordered Banach spaces.
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.
M. M. Talabani (1982)
Colloquium Mathematicae
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V. Lakshmikantham, A. R. Mitchell, R. W. Mitchell (1978)
Annales Polonici Mathematici
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Bertram Yood (2008)
Studia Mathematica
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The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.
Stephen A. Saxon, Albert Wilansky (1977)
Colloquium Mathematicae
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