Results 11 to 20 of about 5,610 (218)
On the Norm Attainment Set of a Bounded Linear Operator and Semi-Inner-Products in Normed Spaces [PDF]
Indian Journal of Pure and Applied Mathematics, 2020 We obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of semi-inner-products to obtain a complete characterization of the norm attainment set of a bounded linear operator between any ...
Debmalya Sain, Sain Debmalya
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Fuzzy Inner Product Space: Literature Review and a New Approach
Mathematics, 2021 The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature.
Sida Lavinia
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Bessel Sequences and Frames in Semi-inner Product Spaces
, 2017 In this paper, the concept of Bessel sequence and frame are introduced in semi-inner product spaces. Some properties of the Bessel sequences and frame are investigated in smooth uniformly convex Banach spaces. One characterization of the space of all Bessel sequences has been pointed out. Examples of frames are constructed in the real sequence spaces \(
Nabin Kumar Sahu +2 more
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Inequalities That Imply the Norm of a Linear Space Is Induced by an Inner Product
Mathematics, 2023 The aim of this paper is to investigate when a linear normed space is an inner product space. Several conditions in a linear normed space are formulated with the help of inequalities. Some of them are from the literature and others are new. We prove that
Marius Radulescu
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A new approach on some operator theory in certain semi-inner-product space
Turkish Journal of Computer and Mathematics Education, 2023 In this note, we assume that F is a linear space over the real or complex number field. The concept of semi-inner product space was introduced in 1961 by G. Lumer [8] but the main properties of it were discovered by J.R. Giles [9], P. L.
S. K. Sahani, Kripa Sindhu Prasad, A. K. Thakur
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Semi-Inner Products and the Concept of Semi-Polarity
Results in Mathematics, 2015 The lack of an inner product structure in general Banach spaces yields the motivation to introduce a semi-inner product with a more general axiom system, one missing the requirement for symmetry, than the one determing a Hilbert space.
Àkos G Horvath +2 more
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Two mappings related to semi-inner products and their applications in geometry of normed linear spaces [PDF]
Applications of Mathematics, 2000 Two mappings associated with the lower and upper semi-inner products \((\cdot ,\cdot)_i\) and \((\cdot ,\cdot)_s\) and with semi-inner product \([\cdot ,\cdot ]\) (in the sense of Lumer) are introduced. The mappings generate the norm of a real normed linear space. Monotonicity and boundedness of these mappings is studied and it is given a refinement of
Silvestru Sever Dragomir +2 more
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Some Refinements of Ostrowski’s Inequality and an Extension to a 2-Inner Product Space
Symmetry, 2019 The purpose of this paper is to prove certain refinements of Ostrowski’s inequality in an inner product space. We study extensions of Ostrowski type inequalities in a 2-inner product space.
Nicusor Minculete, Minculete Nicusor
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On $(n,m)$-$A$-normal and $(n,m)$-$A$-quasinormal semi-Hilbertian space operators [PDF]
Mathematica Bohemica, 2022 The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let ${\mathcal H}$ be a Hilbert space and let $A$ be a positive bounded operator on
Samir Al Mohammady +2 more
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Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces
Axioms, 2023 This paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by a positive semidefinite operator A.
Najla Altwaijry +2 more
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