Results 1 to 10 of about 126 (105)
On the semi-inner product in locally convex spaces [PDF]
International Journal of Mathematics and Mathematical Sciences, 1997 The purpose of this paper is to introduce the concept of semi-inner products in locally convex spaces and to give some basic properties.
Shih-Sen Chang +2 more
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Semi-Inner-Products for Convex Functionals and Their Use in Image Decomposition [PDF]
Journal of Mathematical Imaging and Vision, 2016 Semi-inner-products in the sense of Lumer are extended to convex functionals. This yields a Hilbert-space like structure to convex functionals in Banach spaces. In particular, a general expression for semi-inner-products with respect to one homogeneous functionals is given.
Guy Gilboa, Gilboa Guy
exaly +11 more sources
Involve, 2022 We formalize the notion of vector semi-inner products and introduce a class of vector seminorms which are built from these maps. The classical Pythagorean theorem and parallelogram law are then generalized to vector seminorms that have a geometric mean closed vector lattice for codomain.
Christopher Schwanke
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When are maps preserving semi-inner products linear? [PDF]
Aequationes Mathematicae, 2021 AbstractWe observe that every map between finite-dimensional normed spaces of the same dimension that respects fixed semi-inner products must be automatically a linear isometry. Moreover, we construct a uniformly smooth renorming of the Hilbert space $$\ell _2$$ ℓ 2
Paweł Wójcik, Wójcik Paweł
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Semi-Inner Products and the Concept of Semi-Polarity [PDF]
Results in Mathematics, 2015 The lack of an inner product structure in Banach spaces yields the motivation to introduce a semi-inner product with a more general axiom system, one missing the requirement for symmetry, unlike the one determing a Hilbert space. We use it on a finite dimensional real Banach space $(\X, \| \cdot\|)$ to define and investigate three concepts.
Àkos G Horvath +2 more
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A class of semi-inner products and applications (I)
Journal of Numerical Analysis and Approximation Theory, 1989 Not available.
Sever Silvestru Dragomir
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Generalized semi-inner products with applications to regularized learning
Journal of Mathematical Analysis and Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haizhang Zhang
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Integral Representations of Semi-Inner Products in Function Spaces
International Journal of Analysis and Applications, 2017 Various spaces of measurable functions are usually endowed with semi-inner products expressed in terms of positive measures. Trying to give answers to the inverse problem, we present integral representations for some semi-inner products on function ...
Florian-Horia Vasilescu
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On the Cauchy-Schwarz inequality and its reverse in semi-inner product C*-modules
Banach Journal of Mathematical Analysis, 2007 There are many known Cauchy-Schwarz-type inequalities which are valid in different frameworks. In this paper we consider the A-valued Cauchy-Schwarz inequality and its reverse in a semi-inner product A-module over the C*-algebra A. Some remarks on the A-valued Cauchy-Schwarz inequality in a semi-inner product A-module over the H*-algebra A are also ...
Dijana Ilišević, Sanja Varošanec
exaly +6 more sources
\(L_p\)-\({C}^*\)-semi-inner product spaces
Sahand Communications in Mathematical Analysis, 2022 Summary: This article introduces the notion of \(L_p\)-\({C}^*\)-semi-inner product space, a generalization of the concept of \({C}^*\)-semi-inner product space introduced by \textit{S. S. Gamchi} et al. [Sahand Commun. Math. Anal. 10, No. 1, 73--83 (2018; Zbl 1413.46031)], where we consider Hölder's inequality instead of Cauchy Schwarz' inequality. We
Khalili, Zakiye +3 more
openaire +3 more sources