Orthogonalities, linear operators, and characterization of inner product spaces
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DOI: 10.1007/s00010-017-0494-7
Abstract: It is proved that a normed space, whose dimension is at least three, admitting a nonzero linear operator reversing Birkhoff orthogonality is an inner product space, which releases the smoothness condition in one of J.… read more here.
Keywords: product spaces; product; inner product; orthogonalities linear ... See more keywords
Totally umbilical hypersurfaces of product spaces
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DOI: 10.1007/s00229-021-01339-x
Abstract: Given a Riemannian manifold M, and an open interval I ⊂ R, we characterize nontrivial totally umbilical hypersurfaces of the product M×I — as well as of warped products I ×ω M — as those… read more here.
Keywords: totally umbilical; umbilical hypersurfaces; product spaces; hypersurfaces product ... See more keywords
Few distance sets in ℓp spaces and ℓp product spaces
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DOI: 10.1016/j.ejc.2021.103459
Abstract: Kusner asked if n + 1 points is the maximum number of points in R such that the lp distance (1 < p < ∞) between any two points is 1. We present an improvement… read more here.
Keywords: spaces product; distance; sets spaces; distance sets ... See more keywords
Geometry of product spaces
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125285
Abstract: Abstract We study the inheritance of some geometric properties in a class of normed subspaces of products of normed spaces. This class includes the standard p-direct sums for 1 ≤ p ≤ ∞ . We… read more here.
Keywords: geometry product; product spaces; class; geometry ... See more keywords
Operators on positive semidefinite inner product spaces
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DOI: 10.1016/j.laa.2020.03.004
Abstract: Abstract Let U be a semiunitary space; i.e., a complex vector space with scalar product given by a positive semidefinite Hermitian form 〈 ⋅ , ⋅ 〉 . If a linear operator A : U… read more here.
Keywords: operators positive; product; inner product; semidefinite inner ... See more keywords
Completeness of Inner Product Spaces Associated with Functional on Jordan Structures
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DOI: 10.1134/s1995080220040277
Abstract: Abstract We show that a normal functional $$\varphi$$ on a $$JBW^{\ast}$$ triple induces, via Gelfand–Naimark–Segal like construction, a complete inner product space if and only if $$\varphi$$ is a finite convex combination of extreme points… read more here.
Keywords: completeness inner; inner product; spaces associated; product spaces ... See more keywords
A remark on the ball-covering property of product spaces
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DOI: 10.2298/fil1712905l
Abstract: In this paper, we prove that Banach spaces $X$ and $Y$ have the ball-covering property (BCP) if and only if $(X\times Y, \|\cdot\|_p)$ have the BCP, where $1\leq p \leq\infty.$ read more here.
Keywords: ball covering; property product; covering property; remark ball ... See more keywords
Numerical Radius Inequalities in 2-Inner Product Spaces
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DOI: 10.46793/kgjmat2003.415h
Abstract: In this paper, we have obtained the analogue results on numerical radius inequalities from the classical inner product spaces to 2-inner product spaces. We have established several related reverse inequalities and some well known results… read more here.
Keywords: inner product; inequalities inner; product spaces; radius inequalities ... See more keywords
Some reverses of the Cauchy-Schwarz and triangle inequalities in 2-inner product spaces
Sign Up to like & getrecommendations! Published in 2017 at "Kragujevac journal of mathematics"
DOI: 10.5937/kgjmath1701081o
Abstract: In this paper, we give some reverses of the Cauchy-Schwarz inequality and triangle inequality in 2-inner product spaces. Applications for determinantal integral inequalities are also provided. read more here.
Keywords: triangle; inner product; reverses cauchy; product spaces ... See more keywords