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Communications in algebra, ISSN 0092-7872, 01/2020, Volume 48, Issue 6, pp. 2274 - 2292
It is shown that a finite-dimensional formally real simple Jordan algebra is completely determined by the relation of Jordan-orthogonality. Communicated by... 
Orthogonality
Journal Article
Combinatorica (Budapest. 1981), ISSN 0209-9683, 12/2019, Volume 39, Issue 6, pp. 1425 - 1428
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 11/2018, Volume 2037, Issue 1
This article focuses on introduction the definition of semigeneralized semiderivations of semiprime rings as an additive mapping D : R → R associated with a... 
Orthogonality
Journal Article
Aequationes mathematicae, ISSN 1420-8903, 2011, Volume 83, Issue 1-2, pp. 153 - 189
Journal Article
Lobachevskii journal of mathematics, ISSN 1995-0802, 12/2019, Volume 40, Issue 12, pp. 2111 - 2115
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2017, Volume 454, Issue 1, pp. 59 - 78
Consider a complex normed linear space (X,‖⋅‖), and let χ,ψ∈X with ψ≠0. Motivated by recent works on rectangular matrices and on normed linear spaces, we study... 
Norm | Numerical range | Vector-valued polynomial | Birkhoff–James ε-orthogonality | Birkhoff–James orthogonality | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR POLYNOMIALS | MATRIX POLYNOMIALS | Birkhoff-James orthogonality | Birkhoff-James epsilon-orthogonality
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2015, Volume 431, Issue 2, pp. 1275 - 1284
In this paper, linear ε-orthogonality preserving mappings are studied. We define εˆ(T) as the smallest ε for which T is ε-orthogonality preserving, and then... 
Approximate orthogonality | Orthogonality preserving mappings | Minimum modulus | Isometries | Linear operators | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATELY PRESERVING ORTHOGONALITY
Journal Article
by Paul, K and Sain, D and Ghosh, P
Linear algebra and its applications, ISSN 0024-3795, 2016, Volume 506, pp. 551 - 563
We present a sufficient condition for smoothness of bounded linear operators on Banach spaces for the first time. Let T,A∈B(X,Y), where X is a real Banach... 
Smoothness | Bounded linear operator | Birkhoff–James orthogonality | BirkhoffJames orthogonality | MATHEMATICS | MATHEMATICS, APPLIED | Birkhoff-James orthogonality | SPACES | NORM ATTAINMENT | POINTS
Journal Article
Canadian mathematical bulletin, ISSN 0008-4395, 12/2017, Volume 60, Issue 4, pp. 816 - 829
In this paper, we obtain some characterizations of the (strong) Birkhoff–James orthogonality for elements of Hilbert ${{C}^{*}}$ -modules and certain elements... 
Hilbert C∗-module | Approximate orthogonality | Birkhoff-James orthogonality | Strong Birkhoff-James orthogonality | MATHEMATICS | Hilbert C-module | APPROXIMATELY PRESERVING ORTHOGONALITY | MATRICES | C-ASTERISK-MODULES | MAPPINGS | approximate orthogonality | BOUNDED LINEAR-OPERATORS | strong Birkhoff-James orthogonality
Journal Article
Aequationes mathematicae, ISSN 0001-9054, 6/2016, Volume 90, Issue 3, pp. 647 - 659
We introduce the concept of approximate Roberts orthogonality set and investigate the geometric properties of such sets. In addition, we introduce the notion... 
39B52 | 47B49 | Analysis | Approximate parallelogram law | 46B20 | Mathematics | 46C50 | Combinatorics | a -isosceles-orthogonality | Orthogonality preserving mappings | Approximate Roberts orthogonality | a-isosceles-orthogonality | MATHEMATICS | MATHEMATICS, APPLIED | NORMED SPACES | Mapping | Approximation | Orthogonality | Preserving | Preserves
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2018, Volume 457, Issue 1, pp. 67 - 76
In this paper we explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment. Using Birkhoff–James... 
Linear operator | Smooth Banach space | Norm attainment | Birkhoff–James orthogonality | MATHEMATICS | MATHEMATICS, APPLIED | Birkhoff-James orthogonality | BANACH-SPACES
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 4/2017, Volume 182, Issue 4, pp. 781 - 800
In this paper we study a metric generalization of the sine function which can be extended to arbitrary normed planes. We derive its main properties and give... 
52A10 | 52A21 | 33B10 | Normed plane | 46B20 | Mathematics | Angular bisector | Birkhoff orthogonality | Roberts orthogonality | Isosceles orthogonality | Radon norms | Sine function | Mathematics, general | Antinorm | Minkowski geometry | 32A70 | MATHEMATICS | SPACES | ORTHOGONALITY
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 386, Issue 1, pp. 171 - 176
We define a ρ-orthogonality in a real normed space and we consider the class of linear mappings preserving this relation. We show that a linear mapping... 
Orthogonality in normed spaces | Smooth normed spaces | Orthogonality preserving linear mappings | ρ-Orthogonality
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2020, Volume 360, p. 106896
Weak moonshine for a finite group G is the phenomenon where an infinite dimensional graded G-moduleVG=⨁n≫−∞VG(n) has the property that its trace functions,... 
Moonshine | Group characters | Orthogonality relations | MATHEMATICS
Journal Article
Aequationes mathematicae, ISSN 1420-8903, 2018, Volume 93, Issue 4, pp. 651 - 667
We introduce a generalized orthogonality relation in real normed linear spaces via norm derivatives. The relation between this concept and other types of... 
Analysis | Primary 46B20 | Smooth normed linear spaces | Mathematics | 46C50 | Combinatorics | Norm derivatives | Secondary 39B82 | Birkhoff–James orthogonality | MATHEMATICS | MATHEMATICS, APPLIED | Birkhoff-James orthogonality | Mapping | Derivatives | Vector spaces | Orthogonality
Journal Article
Linear & multilinear algebra, ISSN 1563-5139, 2018, Volume 67, Issue 11, pp. 2147 - 2158
We present a necessary and sufficient condition for the norm-parallelism of bounded linear operators on a Hilbert space. We also give a characterization of the... 
norm-parallelism | Secondary 47L05 | Davis-Wielandt radius | Birkhoff-James orthogonality | numerical radius | Primary 46B20 | Davis–Wielandt radius | Birkhoff–James orthogonality | MATHEMATICS | INEQUALITIES | LOWER BOUNDS | MATRICES | ORTHOGONALITY | Orthogonality | Hilbert space | Linear operators
Journal Article
Journal of Machine Learning Research, ISSN 1532-4435, 2014, Volume 15, pp. 1455 - 1459
Journal Article
Nature materials, ISSN 1476-4660, 2016, Volume 16, Issue 4, pp. 433 - 438
Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for... 
TRANSITION | PHYSICS, CONDENSED MATTER | PHASE | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | SURFACE | CHEMISTRY, PHYSICAL | Crystal defects | Mathematical analysis | Lattices | Photonic crystals | Fluorescence | Visibility | Orthogonality | Parity | Lattice vibration | Propagation modes
Journal Article
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