The Simplest Schemes of Generalized Solution of Linear Operator Equation

D. A. Klyushin (), S. I. Lyashko (), D. A. Nomirovskii (), Yu. I. Petunin () and V. V. Semenov ()
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D. A. Klyushin: Kyiv National Taras Shevchenko University
S. I. Lyashko: Kyiv National Taras Shevchenko University
D. A. Nomirovskii: Kyiv National Taras Shevchenko University
Yu. I. Petunin: Kyiv National Taras Shevchenko University
V. V. Semenov: Kyiv National Taras Shevchenko University

Chapter Chapter 2 in Generalized Solutions of Operator Equations and Extreme Elements, 2012, pp 7-15 from Springer

Abstract: Abstract The purpose of Chap. 2 is to give a natural definition of generalized solution of non-solvable linear operator equation in Banach spaces. In Sects. 2.1–2.4 two concepts of generalized solutions are proposed: strong generalized solution and weak generalized solution based on the duality. In Sect. 2.5 the theorem on existence of a weak generalized solution is proved. The relation between these two approaches is studied in Sect. 2.6 in the case of equations with linear injective operator.

Keywords: Injective Linear Operator; Total Subset; Limit Element; Conjugate Banach Spaces; Hausdorff Topological Vector Space (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0619-8_2

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